Question

A sample of bacteria is growing at an hourly rate of 12% according to the continuous exponential growth function. The sample began with 7 bacteria.

How many bacteria will be in the sample after 20 hours? Round your answer down to the nearest whole number.

Provide your answer below:

Answer 1

68 bacteria

Explanation:

Generally an exponential function with growth can be represented as:
`g(x)=a(1+r)^x`, where r = growth rate, and a = initial value or y-intercept

The growth rate is represented as a decimal, and to convert percentage to decimal, you just divide by 100, so 12% = 12/100 = 0.12, so r = 0.12

Plugging our given values into the equation we get:
`g(x)=7(1.12)^x`. In this function, each time x increases by 1, the value increases by 12%, so the "x" is representing the hours, and to find how much bacteria there is after 20 hours, we simply calculate:
`g(20) = 7(1.12)^(20) \approx 67.524\approx 68`