the population of toledo, ohio, in the year 2000 was approximately 460,000. assume the population is…

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.\na. write the exponential function that relates the total population, ( p(t) ), as a function of ( t ), the number of years since 2000.\n( p(t)= )\nb. use part a. to determine the rate at which the population is increasing in ( t ) years. use exact expressions.\n( p^{prime}(t)= ) people per year\nc. use part b. to determine the rate at which the population is increasing in the year 2015. round to the nearest person per year.\n( p^{prime}(15)= ) people per year

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.\na. write the exponential function that relates the total population, ( p(t) ), as a function of ( t ), the number of years since 2000.\n( p(t)= )\nb. use part a. to determine the rate at which the population is increasing in ( t ) years. use exact expressions.\n( p^{prime}(t)= ) people per year\nc. use part b. to determine the rate at which the population is increasing in the year 2015. round to the nearest person per year.\n( p^{prime}(15)= ) people per year

Answer

Answer:

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