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?

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

Answer 1

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

Answer 2

Option (c) is correct.

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

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+(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+(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,