Solve the problem.
-$$P ( t ) = \frac { 170 } { 1 + 16 e ^ { - 0.188 t } }$$ territory after t years. When will the population be 80?
A)0.1 yr
B)14.12 yr
C)3.48 yr
D)10.74 yr

Question

Quizplus · Accepted Answer

To find when the population will be 80, we set $P(t) = 80$ and solve for $t$. Substituting 80 for $P(t)$ gives us:$$80 = \frac{170}{1 + 16e^{-0.188t}}$$Multiplying both sides by the denominator and then dividing by 80 gives:$$1 + 16e^{-0.188t} = \frac{170}{80}$$$$1 + 16e^{-0.188t} = 2.125$$Subtracting 1 from both sides:$$16e^{-0.188t} = 1.125$$Dividing by 16:$$e^{-0.188t} = \frac{1.125}{16}$$$$e^{-0.188t} = 0.0703125$$Taking the natural logarithm of both sides to solve for $t$:$$-0.188t = \ln(0.0703125)$$$$t = \frac{\ln(0.0703125)}{-0.188}$$$$t \approx 14.12$$ years

Solve the Problem P(t)=1701+16e−0.188tP ( t ) = \frac { 170 } { 1 + 16 e ^ { - 0.188 t } }P(t)=1+16e−0.188t170​

Solve the Problem $P ( t ) = \frac { 170 } { 1 + 16 e ^ { - 0.188 t } }$