The population of a town is 12,000, and it grows at a rate of 5% per year. Write an exponential function in the form y=ab^(x) that represents the situation

Question

The population of a town is 12,000, and it grows at a rate of 5% per year. Write an exponential function in the form
`y=ab^(x)` that represents the situation

Answer 1

Answer: Exponential function:
`y=12000(1.05)^x`

Explanation:

Exponential function:
`y=ab^x` , a = initial value , x= time, b= growth factor , b= 1+r , where r=rate of growth.

Given: Initial population = a= 12,000,

rate of growth = r= 5% = 0.05

Then, b= 1+r= 1+ 0.05 = 1.05

Substitute value of a and b in (i), we get

`y=12000(1.05)^x`

Hence, The required exponential function:
`y=12000(1.05)^x`, where x= time.