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

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,

Answer 2

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