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

Answer:

(a) The population in 2000 is 450

(b) 15% decreases each year

Step-by-step 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

$r = 15\%$