Question 1

Find the present value of the future value.
-$$\mathrm { S } ( \mathrm { t } ) = \mathrm { se } ^ { - 0.018 \mathrm { t } }$$ , where s is the initial amount in grams and t is the time in years since this initial amount was present. If you have a 76-gram piece of this element,
How many grams will you have 4 years from now? Round your answer to the nearest tenth of a
Gram.
A) 0.9 g
B) 81.7 g
C) 70.7 g
D) 37.3 g

Accepted Answer

To find the amount of the element 4 years from now, substitute $s = 76$ grams and $t = 4$ years into the given formula: $$S(t) = 76e^{-0.018 \times 4}$$. Calculating this gives approximately 70.7 grams.

Question 2

Use a graphing calculator to estimate the solution set of the equation. Round to the nearest hundredth.
-$$\left( \frac { 1 } { 3 } \right) ^ { x } = 16$$
A) $\{ - 5.33 \}$
B) $\{ 2.52 \}$
C) $\{ - 0.40 \}$
D) $\{ - 2.52 \}$

Accepted Answer

The answer of Use a graphing calculator to estimate the...

Question 3

Find the present value of the future value.
-$2000, invested for 5 years at 4% compounded quarterly
A) $1659.09
B) $2420.38
C) $2440.38
D) $1639.09

Accepted Answer

The answer of Find the present value of the future...

Question 4

Find the present value of the future value.
-Find the required annual interest rate, to the nearest tenth of a percent, for $1100 to grow to $1400 if interest is compounded monthly for 6 years.
A) 4.0%
B) 0.3%
C) 2.7%
D) 8.1%

Accepted Answer

The formula for compound interest is $A = P(1 + \frac{r}{n})^{nt}$, where $A$ is the amount of money accumulated after n years, including interest, $P$ is the principal amount (the initial amount of money), $r$ is the annual interest rate (decimal), $n$ is the number of times that interest is compounded per year, and $t$ is the time the money is invested for in years. Rearranging the formula to solve for $r$, we get $r = n[(\frac{A}{P})^{\frac{1}{nt}} - 1]$. Substituting $A = 1400$, $P = 1100$, $n = 12$, and $t = 6$ into the formula, we can solve for $r$. After calculation, the rate that rounds to the nearest tenth of a percent is approximately 4.0%.

Question 5

Use a graphing calculator to estimate the solution set of the equation. Round to the nearest hundredth.
-$$3 ^ { x } = 19$$
A) $\{ 6.33 \}$
B) $\{ 0.37 \}$
C) $\{ 1.85 \}$
D) $\{ 2.68 \}$

Accepted Answer

Using a graphing calculator, the solution to the equation $3^x = 19$ is approximately $x = 2.68$.

Question 6

Find the present value of the future value.
-The decay of 291 mg of an isotope is given by A(t)= 291e-0.022t, where t is time in years since the initial amount of 291 mg was present. Find the amount (to the nearest milligram) left after 38 years.
A) 126
B) 63
C) 285
D) 123

Accepted Answer

The amount left after 38 years is calculated using the given decay formula A(t) = 291e^(-0.022t). Substituting t = 38, we get A(38) = 291e^(-0.022*38). Calculating this gives approximately 126 mg (to the nearest milligram).

Question 7

Use a graphing calculator to estimate the solution set of the equation. Round to the nearest hundredth.
-$$e ^ { x } = 7$$
A) $\{ 1.95 \}$
B) $\{ 198.25 \}$
C) $\{ 0.85 \}$
D) $\{ 1096.63 \}$

Accepted Answer

To solve the equation $e^x = 7$, you can use a graphing calculator to graph the function $y = e^x$ and then find the x-value where $y = 7$. The solution is approximately $x = 1.95$, rounding to the nearest hundredth.

Question 8

Find the present value of the future value.
-$6000, invested for 4 years at 3% compounded monthly
A) $6751.97
B) $6763.97
C) $5334.32
D) $5322.32

Accepted Answer

The answer of Find the present value of the future...

Question 9

Find the future value.
-$4013 invested for 9 years at 4.1% compounded quarterly
A) $5761.37
B) $5782.34
C) $5800.30
D) $5793.06

Accepted Answer

The answer of Find the future value.
-$4013 invested for 9...

Question 10

Use a graphing calculator to estimate the solution set of the equation. Round to the nearest hundredth.
-$$e ^ { x } = 2 ^ { x + 1 }$$
A) $\{ 6.52 \}$
B) $\{ - 2.26 \}$
C) $\{ 2.26 \}$
D) $\{ 0.41 \}$

Accepted Answer

The answer of Use a graphing calculator to estimate the...

Question 11

Use a graphing calculator to estimate the solution set of the equation. Round to the nearest hundredth.
-$$5 ( x + 1 ) = 22.00$$
A) $\{ 2.92 \}$
B) $\{ 1.92 \}$
C) $\{ 0.92 \}$
D) $\{ 3.97 \}$

Accepted Answer

The answer of Use a graphing calculator to estimate the...

Question 12

Use a graphing calculator to estimate the solution set of the equation. Round to the nearest hundredth.
-$$3 ^ { 2 x } = 6 ^ { x + 1 }$$
A) $\{ 4.42 \}$
B) $\{ - 2.58 \}$
C) $\{ 2.63 \}$
D) $\{ 1.63 \}$

Accepted Answer

The correct answer is A because the graph of $3 ^ { 2 x } = 6 ^ { x + 1 } $ intersects the $x$-axis at approximately $x = 4.42$.

Question 13

Find the present value of the future value.
-Find the required annual interest rate, to the nearest tenth of a percent, for $5200 to grow to $6500 if interest is compounded quarterly for 7 years.
A) 1.6%
B) 0.8%
C) 4.0%
D) 3.2%

Accepted Answer

To find the required annual interest rate, we use the formula for compound interest: FV = PV(1 + r/n)^(nt). Here, FV = $6500, PV = $5200, n = 4 (quarterly), and t = 7 years. Solving for r gives approximately 3.2% when rounded to the nearest tenth.

Question 14

Find the present value of the future value.
-The growth in the mouse population at a certain county dump can be modeled by the exponential function $$\mathrm { A } ( \mathrm { t } ) = 554 \mathrm { e } ^ { 0.015 \mathrm { t } }$$ , where t is the number of months since the population was first recorded.
Estimate the population after 39 months.
A) 1009
B) 994
C) 562
D) 497

Accepted Answer

The population after 39 months is calculated by substituting t = 39 into the function: A(39) = 554 * e^(0.015 * 39). This evaluates to approximately 994.

Question 15

Find the present value of the future value.
-The sales of a mature product (one which has passed its peak) will decline according to the function $$S ( t ) = S _ { 0 } e ^ { - a t }$$ , where t is time in years since the peak sales. Find the sales of a product 24 years after its peak sales if a = 0.23 and $$\mathrm { S } _ { 0 } = 35,000$$
A) 140 units
B) 10,996,672 units
C) 70 units
D) 44,051 units

Accepted Answer

The correct answer is A because the present value of the future value is 140 units.

Question 16

Find the present value of the future value.
-$$P = \left( \frac { 1 } { 2 } \right) ^ { t / 3.0 }$$ The half-life of Cesium 134m is 3.0 hours. If the formula gives the percent (as a decimal) remaining after time t (in hours), sketch P versus t.  
A)

B)

C)

D)

Accepted Answer

The answer of Find the present value of the future...

Question 17

Use a graphing calculator to estimate the solution set of the equation. Round to the nearest hundredth.
-$$2 ( 4 x - 1 ) = 12$$
A) $\{ 0.93 \}$
B) $\{ 1.15 \}$
C) $\{ 1.75 \}$
D) $\{ 0.65 \}$

Accepted Answer

The answer of Use a graphing calculator to estimate the...

Question 18

Find the present value of the future value.
-The number of reports of a certain virus has increased exponentially since year 0. The number of cases can be approximated using the function $$r ( t ) = 101 e ^ { 0.005 t }$$ where t is the number of years since
Year 0. Estimate the number of cases in year 40.
A) 247 cases
B) 117 cases
C) 123 cases
D) 93 cases

Accepted Answer

The answer of Find the present value of the future...

Question 19

Use a graphing calculator to estimate the solution set of the equation. Round to the nearest hundredth.
-$$2 - x = 5 ^ { - x }$$
A) $\{ 3.06 \}$
B) $\{ - 0.59,1.96 \}$
C) $\{ 2.06 \}$
D) $\{ 1.86 \}$

Accepted Answer

To solve the equation $2 - x = 5^{-x}$ using a graphing calculator, you would graph the two sides of the equation as separate functions and find their points of intersection. The left side, $2 - x$, is a straight line with a negative slope, and the right side, $5^{-x}$, is an exponential decay function. The graph will show two points of intersection, corresponding to the two solutions of the equation. Rounding to the nearest hundredth gives the solutions approximately as $-0.59$ and $1.96$, which matches choice B.

Question 20

Use a graphing calculator to estimate the solution set of the equation. Round to the nearest hundredth.
-$$2 ( x - 1 ) = 18$$
A) $\{ 4.32 \}$
B) $\{ 5.17 \}$
C) $\{ 3.17 \}$
D) $\{ 10.00 \}$

Accepted Answer

The answer of Use a graphing calculator to estimate the...

Quiz 5: Inverse, Exponential, and Logarithmic Functions

Use a graphing calculator to estimate the solution set of the equation. Round to the nearest hundredth. - $\left( \frac { 1 } { 3 } \right) ^ { x } = 16$

Find the present value of the future value. -$2000, invested for 5 years at 4% compounded quarterly

Find the present value of the future value. -Find the required annual interest rate, to the nearest tenth of a percent, for $1100 to grow to $1400 if interest is compounded monthly for 6 years.

Use a graphing calculator to estimate the solution set of the equation. Round to the nearest hundredth. - $3 ^ { x } = 19$

Find the present value of the future value. -The decay of 291 mg of an isotope is given by A(t) = 291e-0.022t, where t is time in years since the initial amount of 291 mg was present. Find the amount (to the nearest milligram) left after 38 years.

Use a graphing calculator to estimate the solution set of the equation. Round to the nearest hundredth. - $e ^ { x } = 7$

Find the present value of the future value. -$6000, invested for 4 years at 3% compounded monthly

Find the future value. -$4013 invested for 9 years at 4.1% compounded quarterly

Use a graphing calculator to estimate the solution set of the equation. Round to the nearest hundredth. - $e ^ { x } = 2 ^ { x + 1 }$

Use a graphing calculator to estimate the solution set of the equation. Round to the nearest hundredth. - $5 ( x + 1 ) = 22.00$

Use a graphing calculator to estimate the solution set of the equation. Round to the nearest hundredth. - $3 ^ { 2 x } = 6 ^ { x + 1 }$

Find the present value of the future value. -Find the required annual interest rate, to the nearest tenth of a percent, for $5200 to grow to $6500 if interest is compounded quarterly for 7 years.

Use a graphing calculator to estimate the solution set of the equation. Round to the nearest hundredth. - $2 ( 4 x - 1 ) = 12$

Use a graphing calculator to estimate the solution set of the equation. Round to the nearest hundredth. - $2 - x = 5 ^ { - x }$

Use a graphing calculator to estimate the solution set of the equation. Round to the nearest hundredth. - $2 ( x - 1 ) = 18$

Quiz 5: Inverse, Exponential, and Logarithmic Functions

Use a graphing calculator to estimate the solution set of the equation. Round to the nearest hundredth. - (13) x=16\left( \frac { 1 } { 3 } \right) ^ { x } = 16(31​) x=16

Find the present value of the future value. -$2000, invested for 5 years at 4% compounded quarterly

Find the present value of the future value. -Find the required annual interest rate, to the nearest tenth of a percent, for $1100 to grow to $1400 if interest is compounded monthly for 6 years.

Use a graphing calculator to estimate the solution set of the equation. Round to the nearest hundredth. - 3x=193 ^ { x } = 193x=19

Find the present value of the future value. -The decay of 291 mg of an isotope is given by A(t) = 291e-0.022t, where t is time in years since the initial amount of 291 mg was present. Find the amount (to the nearest milligram) left after 38 years.

Use a graphing calculator to estimate the solution set of the equation. Round to the nearest hundredth. - ex=7e ^ { x } = 7ex=7

Find the present value of the future value. -$6000, invested for 4 years at 3% compounded monthly

Find the future value. -$4013 invested for 9 years at 4.1% compounded quarterly

Use a graphing calculator to estimate the solution set of the equation. Round to the nearest hundredth. - ex=2x+1e ^ { x } = 2 ^ { x + 1 }ex=2x+1

Use a graphing calculator to estimate the solution set of the equation. Round to the nearest hundredth. - 5(x+1) =22.005 ( x + 1 ) = 22.005(x+1) =22.00

Use a graphing calculator to estimate the solution set of the equation. Round to the nearest hundredth. - 32x=6x+13 ^ { 2 x } = 6 ^ { x + 1 }32x=6x+1

Find the present value of the future value. -Find the required annual interest rate, to the nearest tenth of a percent, for $5200 to grow to $6500 if interest is compounded quarterly for 7 years.

Find the present value of the future value. - P=(12) t/3.0P = \left( \frac { 1 } { 2 } \right) ^ { t / 3.0 }P=(21​) t/3.0 The half-life of Cesium 134m is 3.0 hours. If the formula gives the percent (as a decimal) remaining after time t (in hours) , sketch P versus t.

Use a graphing calculator to estimate the solution set of the equation. Round to the nearest hundredth. - 2(4x−1) =122 ( 4 x - 1 ) = 122(4x−1) =12

Use a graphing calculator to estimate the solution set of the equation. Round to the nearest hundredth. - 2−x=5−x2 - x = 5 ^ { - x }2−x=5−x

Use a graphing calculator to estimate the solution set of the equation. Round to the nearest hundredth. - 2(x−1) =182 ( x - 1 ) = 182(x−1) =18

Use a graphing calculator to estimate the solution set of the equation. Round to the nearest hundredth. - $\left( \frac { 1 } { 3 } \right) ^ { x } = 16$

Use a graphing calculator to estimate the solution set of the equation. Round to the nearest hundredth. - $3 ^ { x } = 19$

Use a graphing calculator to estimate the solution set of the equation. Round to the nearest hundredth. - $e ^ { x } = 7$

Use a graphing calculator to estimate the solution set of the equation. Round to the nearest hundredth. - $e ^ { x } = 2 ^ { x + 1 }$

Use a graphing calculator to estimate the solution set of the equation. Round to the nearest hundredth. - $5 ( x + 1 ) = 22.00$

Use a graphing calculator to estimate the solution set of the equation. Round to the nearest hundredth. - $3 ^ { 2 x } = 6 ^ { x + 1 }$

Use a graphing calculator to estimate the solution set of the equation. Round to the nearest hundredth. - $2 ( 4 x - 1 ) = 12$

Use a graphing calculator to estimate the solution set of the equation. Round to the nearest hundredth. - $2 - x = 5 ^ { - x }$

Use a graphing calculator to estimate the solution set of the equation. Round to the nearest hundredth. - $2 ( x - 1 ) = 18$