Question

a colony contains 1500 bacteria. the population increases at a rate of 115% each hour. if x represents the number of hours elapsed, which function represents the scenario?
f(x) = 1500(1.15)^x
f(x) = 1500(115)^x
f(x) = 1500(2.15)^x
f(x) = 1500(215)^x

Explanation:

Step1: Recall exponential growth formula

The general exponential growth function is $f(x) = P(1 + r)^x$, where $P$ is the initial population, $r$ is the growth rate in decimal, and $x$ is time.

Step2: Convert rate to decimal

Given growth rate is 115% = $\frac{115}{100} = 1.15$

Step3: Calculate growth factor

Growth factor = $1 + r = 1 + 1.15 = 2.15$

Step4: Substitute values into formula

Initial population $P=1500$, so the function is $f(x)=1500(2.15)^x$

Answer:

$f(x) = 1500(2.15)^x$