Question

This exercise uses the population growth model.

The fox population in a certain region has a relative growth rate of 5% per year. It is estimated that the population in 2013 was 16,000.

(a) Find a function

n(t) = n₀e^rt

that models the population t years after 2013.
n(t) =

(b) Use the function from part (a) to estimate the fox population in the year 2020. (Round your answer to the nearest whole number.)


(c) After how many years will the fox population reach 25,000? (Round your answer to one decimal place.)
  yr

(d) Sketch a graph of the fox population function for the years 2013–2021.

Answer 1

The fox population in a certain region has a relative growth rate of st. per year. It is estimated that the population in 2013 was 16000 eft represents the number of years after 2013 and alt) represents the population of fox int years. Then (L (0) = 16000 Relative growth rate is the same as exponential growth rate since relative growth rate depend upon the size of population Relative growth rate r=st. o.ost (a) Hance function net = 16000 e = 0.0S. = (b) To estimate fox population in the year 2020 t=2020-2013 = 7 0.0SC7) 0.35 167) 16000 e = 16000 xe 22,70S NLT) 22.505. Population in year 2020 when nit) = 22.505 25000 asooo = 16000 boost 25000 o.ost 25 - ( C ) 16ooo = e e ln (252) Taking logarith o.ost = t- aos en (25) 8.9257 & 8.9 years. Population reaches 2000 after [8.9 years a) sketch on graph shoot.