QuestionThe fox population in a certain region has an annual growth rate of 5 percent per year. (Note: Foxes mate once per year.)
It is estimated that the fox population in the year 2020 was 14000.
(a) Find an exponential function that models the fox population years after 2020 (Note: for 2020). The function is
(b) Use the function from part (a) to estimate the fox population in the year 2028. (The answer should be an integer.)
There will be foxes in the year 2028.
Studdy Solution
STEP 1
1. The fox population grows exponentially at a rate of 5% per year.
2. The initial population in the year 2020 is 14,000 foxes.
3. We need to find the population function and estimate the population in 2028.
STEP 2
1. Determine the exponential growth function.
2. Calculate the fox population for the year 2028 using the function.
STEP 3
The general form of an exponential growth function is , where is the initial population, is the growth rate, and is the time in years.
STEP 4
Given and (5% growth rate), substitute these values into the general form to get the specific function for this problem:
STEP 5
To find the population in the year 2028, calculate as the number of years after 2020. Thus, .
STEP 6
Substitute into the function to find the population in 2028:
STEP 7
Calculate .
STEP 8
Calculate .
STEP 9
Since the population must be an integer, round to the nearest whole number. Thus, the estimated fox population in 2028 is 20,684.
The exponential function is:
The estimated fox population in 2028 is:
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