Question

Suppose the population in a town has an average growth rate of 18% . If there are 15,500 people now living in town, in about how many years will the population grow to 30,000? Use the equation 30,000 = (15,500)(1.18)x and round the value of x to the nearest year.

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Answer 1

Option C. 4 years

Explanation:

Population growth of a town is described by the equation

`30000=(15500)(1.18)^(x)`

where x is the number of years.

Now we have to calculate the duration after which population of the town will be 30000 with an average growth rate of 18%.

We will use the equation to get the value of x.

`30000=(15500)(1.18)^(x)`

`1.18^(x)=(30000)/(15500)=1.94`

Now we take log on both the sides of the equation.

Log(1.94) = xlog(1.18)

0.2878 = .0719x

`x = (0.2878)/(0.0719)=4`

Therefore after 4 years population of the town will be 30000.