Question

The population of Bengal tigers in a region of India can be modeled by the function P = 450(0.85), where P is the

population and I is the number of years since 2000.
What is the Bengal tiger population in 2000?
and by what percent does the tiger population decrease each year?

Answer 1

(a) The population in 2000 is 450

(b) 15% decreases each year

Explanation:

Given

`P = 450(0.85)^t` --- since 2000

`P \to Population`

`t \to years`

Solving (a): The population in 2000

First calculate t

`t = 2000 - 2000` --- years since 200

`t = 0`

So, we have:

`P = 450(0.85)^t`

`P = 450 * 0.85^0`

`P = 450 * 1`

`P = 450`

Solving (b): Rate of population decrease

A function that decreases is represented as:

`P(t) = a(1 - r)^t`

Where

`r \to` rate of decrement

Compare
`P(t) = a(1 - r)^t` and
`P = 450(0.85)^t`

`1- r = 0.85`

Collect like terms

`r = 1 - 0.85`

`r = 0.15`

Express as percentage

`r = 15\%`