Question 1

Solve the problem.
-In North America, coyotes are one of the few species with an expanding range. The future population of coyotes in a region of Mississippi valley can be modeled by the equation P = 59 + 12 · ln(18t + 1), where t is time in
Years. Use the equation to determine when the population will reach 170. (Round your answer to the nearest
Tenth year.)
A) 578.0 years
B) 586.2 years
C) 583.1 years
D) 581.3 years

Accepted Answer

The answer of Solve the problem.
-In North America, coyotes are...

Question 2

Solve the problem.
-Book sales on the Internet (in billions of dollars) in year x are approximated by f(x) = 1.84 + 2.1 · ln x, where x = 0 corresponds to 2000. How much will be spent on Internet book sales in 2008? Round to the nearest tenth.
A) 8.0 billion
B) 6.2 billion
C) 6.0 billion
D) 3.9 billion

Accepted Answer

In 2008, x = 8. Plug x = 8 into the function: f(8) = 1.84 + 2.1 · ln(8). Calculate ln(8) ≈ 2.079. Then, f(8) ≈ 1.84 + 2.1 * 2.079 ≈ 6.2 billion.

Question 3

Solve the problem.
-U. S. Census Bureau data shows that the number of families in the United States (in millions) in year x is given by h(x)  980. How many families were there in 2002?
A) 48 million
B) 72 million
C) 21 million
D) 90 million

Accepted Answer

To find the number of families in the year 2002, we need to plug in x = 2002 into the given function h(x).

h(2002) = 11e^(0.014(2002-1960)) = 11e^(0.014(42)) = 72 million

Therefore, there were approximately 72 million families in the United States in the year 2002. So, the best choice is B.

Question 4

Solve the problem.
-The level of a sound in decibels (db) is determined by the formula he formula  ) db, where I db, where Iis the intensity of the sound in watts per square meter. A certain noise has an intensity of 8.49 × 10-4 watts per square
Meter. What is the sound level of this noise? (Round your answer to the nearest decibel.)
A) 89 db
B) 206 db
C) 79 db
D) 9 db

Accepted Answer

The answer of Solve the problem.
-The level of a sound...

Question 5

Solve the problem.
-A country has a population growth rate of 2.4% compounded continuously. At this rate, how long will it take for the population of the country to double? Round your answer to the nearest tenth.
A) .29 years
B) 30 years
C) 2.9 years
D) 28.9 years

Accepted Answer

We can use the formula for continuous compounding to solve this problem, which is:

A = Pe^(rt)

Where A is the final amount, P is the initial amount, e is the mathematical constant roughly equal to 2.71828, r is the annual interest rate (or growth rate), and t is the time in years.

We want to know how long it will take for the population to double, which means the final amount A will be twice the initial amount P. So we can write:

2P = Pe^(0.024t)

Simplifying, we can divide both sides by P:

2 = e^(0.024t)

Taking the natural logarithm of both sides, we get:

ln(2) = 0.024t

Solving for t, we get:

t = ln(2)/0.024 ≈ 28.9 years

So it will take about 28.9 years for the population to double, which is the closest choice to our answer. The correct answer is D. We can use the continuous compound interest formula, which has the same form as the population growth formula:
A = Pe^(rt)
where A is the final amount, P is the initial amount, e is the base of the natural logarithm, r is the growth rate, and t is time.
If we let A = 2P (since we want to know when the population doubles), P = 1 (since we are using a relative growth rate), and r = 0.024 (since the growth rate is 2.4%), we can solve for t:
2 = e^(0.024t)
ln(2) = 0.024t
t = ln(2)/0.024 ≈ 28.9 years

Question 6

Solve the problem.
-Assume that a savings account earns interest at the rate of 2% compounded monthly. If this account contains $1000 now, how many months will it take for this amount to double if no withdrawals are made?
A) 417 months
B) 12 months
C) 408 months
D) 450 months

Accepted Answer

The amount of money in the account after t months is given by the formula A = 1000(1 + 0.02/12)^12t. We want to find t such that A = 2000. Substituting this into the formula, we get 2000 = 1000(1 + 0.02/12)^12t. Dividing both sides by 1000, we get 2 = (1 + 0.02/12)^12t. Taking the logarithm of both sides, we get log(2) = 12t * log(1 + 0.02/12). Dividing both sides by 12 * log(1 + 0.02/12), we get t = log(2) / (12 * log(1 + 0.02/12)) ≈ 417. Therefore, it will take approximately 417 months for the amount in the account to double.

Question 7

Solve the problem.
-A carbon-14 dating test is performed on a fossil bone, and analysis finds that 15.5% of the original amount of carbon-14 is still present in the bone. Estimate the age of the fossil bone. (Recall that carbon-14 decays
According to the equation  )).
A) 1,500 years
B) 15, 000 years
C) 15,035 years
D) 150 years

Accepted Answer

The formula for exponential decay is A = A0e^(-kt), where A is the present amount, A0 is the initial amount, k is the decay constant, and t is time. Solving for t, we get t = ln(A/A0) / (-k). Using data from the problem, we know that A/A0 = 0.155 (since 15.5% of the original amount is still present). The half-life of carbon-14 is about 5,700 years, which means the decay constant k is ln(0.5)/5700 = 0.000121. Plugging in these values, we get t = ln(0.155)/(-0.000121) = 15,035 years. Therefore, the best choice is C. The half-life of carbon-14 is approximately 5,700 years. If 15.5% of the original amount of carbon-14 is still present, this means that the bone has gone through approximately 3 half-lives (since each half-life reduces the amount of carbon-14 by half). Therefore, we can estimate the age of the fossil bone by multiplying 3 half-lives by 5,700 years per half-life, giving an estimated age of 17,100 years. However, we must also account for the fact that carbon-14 is constantly being replenished in the atmosphere, so the age estimate may be slightly younger. Taking this into account, the best choice is C) 15,035 years, which is closest to the estimated age of the bone.

Question 8

Solve the problem.
-If $4,000 is invested at 7% compounded annually, how long will it take for it to grow to $6,000, assuming no withdrawals are made? Compute answer to the next higher year if not exact. 
A) 2 years
B) 5 years
C) 8 years
D) 6 years

Accepted Answer

The answer of Solve the problem.
-If $4,000 is invested at...

Quiz 2: Limits and the Derivative

Solve the problem. -Book sales on the Internet (in billions of dollars) in year x are approximated by f(x) = 1.84 + 2.1 · ln x, where x = 0 corresponds to 2000. How much will be spent on Internet book sales in 2008? Round to the nearest tenth.

Solve the problem. -U. S. Census Bureau data shows that the number of families in the United States (in millions) in year x is given by h(x) 980. How many families were there in 2002?

Solve the problem. -A country has a population growth rate of 2.4% compounded continuously. At this rate, how long will it take for the population of the country to double? Round your answer to the nearest tenth.

Solve the problem. -Assume that a savings account earns interest at the rate of 2% compounded monthly. If this account contains $1000 now, how many months will it take for this amount to double if no withdrawals are made?

Solve the problem. -A carbon-14 dating test is performed on a fossil bone, and analysis finds that 15.5% of the original amount of carbon-14 is still present in the bone. Estimate the age of the fossil bone. (Recall that carbon-14 decays According to the equation ) ) .

Solve the problem. -If $4,000 is invested at 7% compounded annually, how long will it take for it to grow to $6,000, assuming no withdrawals are made? Compute answer to the next higher year if not exact.