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

Answer:

68 bacteria

Step-by-step 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: $g(20) = 7(1.12)^{20} \approx 67.524\approx 68$