Question

the population of toledo, ohio, in the year 2000 was approximately 460,000. assume the population is increasing at a rate of 4.6% per year.
a. write the exponential function that relates the total population, ( p(t) ), as a function of ( t ), the number of years since 2000.
( p(t)= )
b. use part a. to determine the rate at which the population is increasing in ( t ) years. use exact expressions.
( p^{prime}(t)= ) people per year
c. use part b. to determine the rate at which the population is increasing in the year 2015. round to the nearest person per year.
( p^{prime}(15)= ) people per year

Explanation:

Answer:

(a) \( P(t) = 460000e^{0.046t} \)
(b) \( P'(t) = 21160e^{0.046t} \)
(c) \( P'(15) = 41171 \)