a colony contains 1500 bacteria. the population increases at a rate of 115% each hour. if x represents the…

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?\n○ (f(x)=1500(1.15)^x)\n○ (f(x)=1500(115)^x)\n○ (f(x)=1500(2.15)^x)\n○ (f(x)=1500(215)^x)

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?\n○ (f(x)=1500(1.15)^x)\n○ (f(x)=1500(115)^x)\n○ (f(x)=1500(2.15)^x)\n○ (f(x)=1500(215)^x)

Answer

Explanation:

Step1: Identify the initial amount and growth - rate formula

The initial population of bacteria $a = 1500$. The general formula for exponential growth is $f(x)=a(1 + r)^x$, where $a$ is the initial amount, $r$ is the growth rate as a decimal, and $x$ is the number of time - intervals.

Step2: Convert the percentage to a decimal

The growth rate is $115%$. To use it in the formula, we convert it to a decimal. $r=\frac{115}{100}=1.15$.

Step3: Substitute values into the formula

Substitute $a = 1500$ and $r = 1.15$ into the formula $f(x)=a(1 + r)^x$. We get $f(x)=1500(1 + 1.15)^x=1500(2.15)^x$.

Answer:

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