The true statements about the functions are:
- b. The population of the city in 2010 is 25000
- c. The rate at which the population decreases every year is 4%
- f. The function value would approach 0 as it decreases
How to determine the true statement?
The function is given as:
f(x) = 25000 * 0.96^x
Set x = 0 to determine the initial value of the function
f(0) = 25000 * 0.96^0
Evaluate
f(0) = 25000
This means that the population of the city in 2010 is 25000 i.e. option (B) is correct
Also, we have:
f(x) = 25000 * 0.96^x
The rate at which the population decreases every year is calculated as:
r = 1 - 0.96
Evaluate the difference
r = 0.04
Express as percentage
r = 4%
This means that the rate at which the population decreases every year is 4% i.e. option (C) is correct
The population after 5 and 10 years are:
f(5) = 25000 * 0.96^5
f(5) = 20384
f(10) = 25000 * 0.96^10
f(10) = 16621
Divide these populations by the initial population in 2010
20384/25000 = 82%
16621/25000 = 66%
This means that the population decreased by 82% and 66% in 5 years and 10 years since 2010, respectively.
So, options (d) and (e) are false
Lastly, because the population function is an exponential decay function;
The function value would approach 0 as it decreases
This means that option (f) is correct
Read more about exponential decay function at
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