type the correct answer in the box. when the county fair opened its gates, 68 people entered the…

type the correct answer in the box. when the county fair opened its gates, 68 people entered the fairgrounds. after one hour, there were 1.5 times as many people on the fairgrounds as when the gates opened. after two hours, there were 1.5 times as many people on the fairgrounds as the previous hour. if this pattern continues, write the function representing the number of people, f(x), at the fair x hours after the gates open. f(x) =

type the correct answer in the box. when the county fair opened its gates, 68 people entered the fairgrounds. after one hour, there were 1.5 times as many people on the fairgrounds as when the gates opened. after two hours, there were 1.5 times as many people on the fairgrounds as the previous hour. if this pattern continues, write the function representing the number of people, f(x), at the fair x hours after the gates open. f(x) =

Answer

Explanation:

Step1: Identify the initial - value

The initial number of people when the gates opened is $a = 68$.

Step2: Identify the common - ratio

The number of people is multiplied by a factor of $r=1.5$ each hour.

Step3: Write the exponential function formula

The general form of an exponential function is $f(x)=a\cdot r^{x}$, where $a$ is the initial value and $r$ is the common ratio. Substituting $a = 68$ and $r = 1.5$ into the formula, we get $f(x)=68\cdot(1.5)^{x}$.

Answer:

$f(x)=68\cdot(1.5)^{x}$