Question

PLEASE HELP!! 30 POINTS

Answer 1

Answer:

a) $N(t) = 35e^{0.18t}$

b) The projected population after 6 years is of 103 stray cats.

c) The number of years required for the stray-cat population to reach 700 is 16.64.

Step-by-step explanation:

The population N(t) after t years, following an exponential growth moel, is given by:

$N(t) = N(0)e^{rt}$

In which N(0) is the initial population and r is the growth rate.

In 1999 the town had 35 stray cats, and the relative growth rate was 18% per year.

This means that $N(0) = 35, r = 0.18$

(a) Find the function that models the stray-cat population n(t) after t years.

$N(t) = N(0)e^{rt}$

$N(t) = 35e^{0.18t}$

(b) Find the projected population after 6 years.

This is N(6).

$N(t) = 35e^{0.18t}$

$N(6) = 35e^{0.18*6}$

$N(6) = 103$

The projected population after 6 years is of 103 stray cats.

(c) Find the number of years required for the stray-cat population to reach 700.

This is t for which N(t) = 700. So

$N(t) = 35e^{0.18t}$

$700 = 35e^{0.18t}$

$e^{0.18t} = \frac{700}{35}$

$e^{0.18t} = 20$

$\ln{e^{0.18t}} = \ln{20}$

$0.18t = \ln{20}$

$t = \frac{\ln{20}}{0.18}$

$t = 16.64$

The number of years required for the stray-cat population to reach 700 is 16.64.