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?

Julius
Jan 10, 2018

#3**+2 **

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

hectictar
Jan 10, 2018

#3**+2 **

Best Answer

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

hectictar
Jan 10, 2018