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 ttps://tex.z-dn.net/?f=y%3Dab%5E%7Bx%7D" id="TexFormula1" title="y=ab^{x}" alt="y=ab^{x}" align="absmiddle" class="latex-formula"> that represents the situation

Answer 1

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

Step-by-step 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.