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(2.15)^x )
( f(x) = 1500(1.15)^x )
( f(x) = 1500(215)^x )
( f(x) = 1500(115)^x )

Explanation:

Step1: Recall growth function form

The exponential growth formula is $f(x) = P(1+r)^x$, where $P$ is initial population, $r$ is growth rate (decimal).

Step2: Convert rate to decimal

$115\% = \frac{115}{100} = 1.15$

Step3: Substitute values into formula

$P=1500$, $r=1.15$, so $f(x)=1500(1+1.15)^x = 1500(2.15)^x$

Answer:

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