Question

The fox population in a certain region has a relative growth rate of 6% per year. It is estimated that the population in 2013 was 18,000. (a) Find a function n(t) = n0ert 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 2018. (Round your answer to the nearest whole number.) foxes (c) After how many years will the fox population reach 24,000? (Round your answer to one decimal place.) yr

Answer 1

Answer:

Step-by-step explanation:

initial population, n0 = 18000

rate of growth, r = 6% = 6/100 = 0.06

a) The function that models the population t years after 2013 would be

n(t) = 18000e0.06t

b)In 2018, the number of years, t = 2018 - 2013 = 5 years

The population would be

n(t) = 18000e0.06 × 5

n(t) = 18000e0.3

n(t) = 24297

c) n(t) = 24000

Therefore

24000 = 18000e0.06t

24000/18000 = e0.06t

1.33 = e0.06t

Take ln on both sides of the equation, it becomes

0.285 = 0.06t

t = 0.285/0.06

t = 4.75 years