Question

he California Tiger Salamander is an endangered species, which decreases at the rate of 4.6% per year in a habitat that currently has 60 of them. Write an exponential function and find how many California Tiger Salamanders will be left after 4 years.

Answer 1

There will be approximately 50 California Tiger Salamanders left after 4 years.

Explanation

General exponential decay formula is......

$y(t)= a*e^-^k^t$ , where $y(t)$ is the value at time 't' , $a$ is the initial value , $k$ is the rate of decay in decimal and $t$ is the time.

The number of California Tiger Salamander decreases at the rate of 4.6% per year. That means, the decay rate$(k) =4.6\%= 0.046$

In the habitat, there is currently 60 tigers. So, the initial value$(a) = 60$

So, the exponential function will be now......

$y(t)= 60*e^-^0^.^0^4^6^t$

Now for finding the number of tigers after 4 years, we will just plug $t=4$ into the above equation. So.....

$y(4)=60*e^-^0^.^0^4^6^*^4\\ \\ y(4)= 60* e^-^0^.^1^8^4\\ \\ y(4)=49.916....\approx 50$

Thus, there will be approximately 50 California Tiger Salamanders left after 4 years.