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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?



A f(x) = 1500(1.15)x


B f(x) = 1500(115)x


C f(x) = 1500(2.15)x


D f(x) = 1500(215)x

Verified Answer :

ddixon0665

its  f(x)=1500(2.15)x so c hope this helps

Answer:

Option (c) is correct.

\(f(x)=1500(2.15)^x\) function representing the increase of bacteria every hour x,

Step-by-step explanation:

Given : A colony contains 1500 bacteria. The population increases at a rate of 115% each hour.

we have to find the function that represents the given scenario.

Let x represents the number of hours elapsed.

Given  A colony contains 1500 bacteria

 and number of bacteria is increasing at a rate of 115% each hour.

Using formula for Compound interest , we have,

\(A=P(1+\frac{r}{100} )^t\)

Where A is amount

T is time period

R is rate of interest

Here, P = 1500

T = x hours

R = 115%

Let f(x) be the function representing the increase of bacteria every hour.

Substitute, we have,

\(f(x)=1500(1+\frac{115}{100} )^x\)

Simplify, we get,

\(f(x)=1500(1+1.15)^x\)

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

Thus, \(f(x)=1500(2.15)^x\) function representing the increase of bacteria every hour x,

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