In 2009 there was an endangered population of 270 cranes in a western state. due to wildlife efforts, the population is increasing at a rate of 5% per year.
a. what exponential function would be a good model for this population of cranes?
b. if this trend continues, how many cranes will there be in this population in 2020?

Assuming compount interest format

for compounded per 1 year
A=future amount
P=present amount
r=rate in decimal
t=time in years

given
P=270
r=5%=0.05

the equaton is
or

for any year, 2009, is year 0, so if you wanted to input the year then
would be for t=what year it was

A.

b. 2009 to 2020
2020-2009=11 years
t=11

f(11)=461.792
about 462 cranes

A.
B. about 462

Given function:

p(t) = 2³

a)

Find x when p(t) = 200:

2³ = 200 = 2522t/3 = log 25t = 3 log 5t = 2.0969 years ≈ 2 years and 1 month

b)

Find p(t) when t = 4:

p(4) = 2³( ) = 8* = 3713.27 million