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# Rate of Change?

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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?

Jan 10, 2018

#3
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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 Jan 10, 2018

#1
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yes you are correct

Jan 10, 2018
#2
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Are you just making stuff up or?

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