Question

the fox population in a certain region has a relative growth rate of 9% per year. it is estimated that the population in 2013 was 17,000. (a) estimate the fox population in the year 2019. (round your answer to the nearest whole number.) foxes (b) after how many years will the fox population reach 22,000? (round your answer to one decimal place.)

Answer 1

Part a

The estimated population of fox in the year 2019  is 28511

Part b

The after 3 years the population will reach 22000

The population in 2013 = 17000

The growth rate = 9% per year

Therefore it is an exponential function

Consider the P(x) as the population in x years

The the exponential function

P(x) = 17000 × $(1+0.09)^x$

We have to find the population in 2019

Number of years = 6

Substitute the values in the function

P(6) = 17000 × $(1.09)^6$

= 28510.7

≈ 28511

Part b

The population of fox = 22000

22000 = 17000 × $1.09^x$

$1.09^x$ = 22000/17000

$1.09^x$ = 22/17

x = ln (22/17) / ln(1.09)

x = 2.99

x ≈ 3 years

Hence,

Part a

The estimated population of fox in the year 2019  is 28511

Part b

The after 3 years the population will reach 22000

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