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

Answer 1

Explanation:

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(1.15)x

f(x) = 1500(115)x

f(x) = 1500(2.15)x

f(x) = 1500(215)x

The answer to this problem is a f(x) = 1500(2.15)x

Answer 2

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

Explanation:

Let the function that represents the population of bacteria after x hours is,

`f(x)=ab^x`

For x = 0, f(x) = 1500,

`1500=a(1+r)^0`

`1500=a`

Now, the population increases at a rate of 115% each hour,

So, the population after 1 hour = (100+115)% of 1500 = 215% of 1500 = 3225,

That is, for x = 1, f(x) = 3225,

`3225 =ab`

`3225=1500(b)`

`\implies b =2.15`

Hence, the function that represents the given scenario is,

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