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Twenty years ago a small town in Texas had a population of 10,000. The population has increased 8% each year since then. What is the growth factor that would be used to solve this problem?

Respuesta :

kphung76127
The growth factor is one plus or minus (depending on increase or decrease) the percent written as a decimal. In this case 1-0.08= 0.92

Answer:

1.08

Step-by-step explanation:

We have been given that 20 ears ago a small town in Texas had a population of 10,000. The population has increased 8% each year since then.

We can see that population is increasing exponentially, so we will use exponential function to write formula for our given information.

[tex]y=a*(b)^x[/tex], where,

a = Initial value,

b = For growth b is in form (1+r), where r is growth rate in decimal form.

Let us convert our given growth rate in decimal form.

[tex]8\%=\frac{8}{100}=0.08[/tex]

Upon substituting our given values in exponential function formula we will get,

[tex]y=10,000*(1+0.08)^x[/tex]

[tex]y=10,000*(1.08)^x[/tex]

We can see that value of b is 1.08, therefore, growth factor for our given problem is 1.08.

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