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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 [tex]y=ab^{x}[/tex] that represents the situation

Respuesta :

JeanaShupp

Answer: Exponential function: [tex]y=12000(1.05)^x[/tex]

Step-by-step explanation:

Exponential function: [tex]y=ab^x[/tex] , 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

[tex]y=12000(1.05)^x[/tex]

Hence, The required exponential function: [tex]y=12000(1.05)^x[/tex], where x= time.