+956 The population of a town is increasing at a rate of 1.4% annually. The current population of the town is 2 000. Calculate the average rate of change over the next 10 years.
a) 31.95 people/year
b) 2 298 people/year
c) 30 people/year
d) 298 people/year
I did this:
A=2000(1+0.014)^10
A=2298
Is that correct?
+9464 num of people after 0 years = 2000
num of people after 10 years = 2000(1 + 0.014)10 = 2000(1.014)10
The number you calculated is the population after 10 years...now we need the avg rate of change.
avg rate of change = \(\frac{\text{change in num of people}}{\text{change in num of years}}\)
avg rate of change = \(\frac{2000(1.014^{10})\,-\,2000}{10\,-\,0}\) people/year
avg rate of change ≈ 29.831 people/year ≈ 30 people/year 
+9464 num of people after 0 years = 2000
num of people after 10 years = 2000(1 + 0.014)10 = 2000(1.014)10
The number you calculated is the population after 10 years...now we need the avg rate of change.
avg rate of change = \(\frac{\text{change in num of people}}{\text{change in num of years}}\)
avg rate of change = \(\frac{2000(1.014^{10})\,-\,2000}{10\,-\,0}\) people/year
avg rate of change ≈ 29.831 people/year ≈ 30 people/year
