Question

the population of a deer in the national park in model by the equation P = 300e^(it). If the population of the deer is 400 after 2 years, find the value of k. Round your answer to the nearest hundredth. NO LINKS!!!​

Answer 1

k ≈ 0.14

Explanation:

Given

P = 300
`e^(kt)`

Substitute P = 400 and t = 2 into the equation

400 = 300
`e^(2k)` ( divide both sides by 400 )

`e^(2k)` =
`(4)/(3)` ( take ln of both sides )

ln
`e^(2k)` = ln (
`(4)/(3)` )

2k = ln (
`(4)/(3)` ) ( divide both sides by 2 )

k =
`(ln(4)/(3) )/(2)` ≈ 0.14 ( to the nearest hundredth )