Answer:
a)
Growth rate 0.075
Growth factor 1.075
b) 59177 or approx 60000
Step-by-step explanation:
I love these kind of question where we get to model equations :D So lets get started.
a)
The population of a city after t years after 2010 is given by
[tex]P=20000(1.075)^t[/tex]
The original exponential growth formula is:
[tex]y=a(1+r)^t[/tex]
so we can write our equation in this form as well:
[tex]P=20000(1+0.075)^t[/tex]
the growth factor is 1+r which is 1+0.075 which is 1.075
the growth rate is determined by the value of r which is 0.075
b)
Since our equation represents the population of a city after the year 2010 we can use it to further calculate the population in 2025 so
2025 - 2010 = 15
we set the value of t in our equation to 15 which is in years,
[tex]P=20000(1.075)^{15}\\P=59177[/tex]
so we can say that our population in 2025 would be approximately 60,000
