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:
[tex]P(t)=P_0(1-r)^t[/tex]
Where A is the population at any time t.
[tex]P_0[/tex] is the initial population so [tex]P_0=100000[/tex]
r is the rate of decrease so r=2%=0.02
t is the number of years
Now plug those values, we get:
[tex]P(t)=100000(1-0.02)^t[/tex]
[tex]P(t)=100000(0.98)^t[/tex]
Hence required function is [tex]P(t)=100000(0.98)^t[/tex].
