Question

The number of bacteria in a culture after t hours is modeled by the function n(t)=500e^0.15t How many bacteria are present after 12 hours? Remember to round to the nearest bacteria.

Answer 1

To calculate the number of bacteria after 12 hours, we plug in the value of 12 into the growth function n(t) = 500e^0.15t, resulting in approximately 3025 bacteria after rounding to the nearest whole number.

Step-by-step explanation:

To find the number of bacteria present after 12 hours using the given model n(t) = 500e^0.15t, we substitute the value of t with 12.

Therefore, n(12) = 500e^(0.15×12)

= 500e^1.8.

Using a calculator to compute e^1.8 and then multiplying by 500 gives us the number of bacteria at 12 hours. It is important to round to the nearest whole number as we cannot have a fraction of a bacterium.

Thus, the calculation will result in the population of bacteria after 12 hours:

n(12) = 500×e^1.8

≈ 500×6.04964746

= 3024.82373, which we round to 3025 bacteria.