Algebra

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 18,000.
(a) Find a function
n(t) = n0ert
that models the population t years after 2013.
n(t) =

Correct: Your answer is correct.


(b) Use the function from part (a) to estimate the fox population in the year 2021. (Round your answer to the nearest whole number.)
26853

Correct: Your answer is correct.
foxes

(c) After how many years will the fox population reach 27,000? (Round your answer to one decimal place.)
8

Incorrect: Your answer is incorrect.
yr

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

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  1. a 5% growth per year, starting at 18000 means n(t) = 18000 * 1.05^t
    Since 1.05 = e^(ln 1.05) that makes
    n = 18000 (e^(ln 1.05))^t
    n = 18000 e^(ln 1.05 * t)
    n = 18000 e^(.0488t)
    Now you can answer the other questions.

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    oobleck
  2. looks like you missed d)
    18000 e^(0.05t) = 27000
    e^(.05t) = 1.5
    take ln of both sides and use log rules
    .05t = ln1.5
    t = ln1.5/.05 = appr 8.1 years past 2013

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    Reiny

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