Question

23. A population of mice grows according to the formula A(t) = 300e0.087t where

t is measured in months. Determine the amount of mice when t = 0.
a) O mice
b) 300 mice
c) 87 mice
d) 900 mice

Answer 1

Option B

The amount of mice when t = 0 is 300

Solution:

Given that population of mice grows according to the formula:

`A(t) = 300e^(0.087t)`

where t is measured in months

To find: amount of mice when t = 0

So we have to substitute t = 0 in given formula and find value of A(t)

`A(t) = 300e^(0.087t)`

Substitute t = 0

`A(t) = 300e^(0.087 * 0)\\\\A(t) = 300e^(0)`

`\text{ We know that } e^0 = 1`

So we get,

`A(t) = 300 * 1 = 300`

Thus the amount of mice when t = 0 is 300