Question

Write a function in terms of t that represents the situation.

Answer 1

Given that opulation of 100,000 decreases by 2% each year.

Now question says to write a function in terms of t that represents the situation.

Question is talking about population decrease so we can apply decay formula. which is given by:

$P(t)=P_0(1-r)^t$

Where A is the population at any time t.

$P_0$ is the initial population so $P_0=100000$

r is the rate of decrease so r=2%=0.02

t is the number of years

Now plug those values, we get:

$P(t)=100000(1-0.02)^t$

$P(t)=100000(0.98)^t$

Hence required function is $P(t)=100000(0.98)^t$.