Question

Ju Wenjun is an ecologist who studies the change in the tiger population of Siberia over time. The relationship between the elapsed time ttt, in years, since Ju Wenjun started studying the population, and the number of tigers, N(t)N(t)N, left parenthesis, t, right parenthesis, is modeled by the following function N(t)=650⋅(1625)t

Complete the following sentence about the rate of change in the tiger population.
Round your answer to two decimal places.
The number of tigers decays by a factor of \dfrac45
5
4
​
start fraction, 4, divided by, 5, end fraction every

Answer 1

0.50 years

Step-by-step explanation:

got it correct on khan

Answer 2

The number of tigers decays by a factor of

`(4)/(5)` every 0.50 years

Step-by-step explanation:

The correctly written function is

`N(t)=650\cdot \bigg((16)/(25)\bigg)^t`

Convert 16/25 into its equivalent form (4/5)²

`N(t)=650\cdot \bigg((4)/(5)\bigg)^(2t)`

If you make t = 1/2, this is half-year, the population of tigers will decay by a factor of 4/5 in that time. Every time the half-year passes, the population is multiplied by 4/5, which means that the polulation will decay by a factor of 4/5 whenever half a year elapses.

Hence, the number of tigers decays by a factor of 4/5 every 0.50 years.