Question

When you grow a culture of bacteria in a Petri dish, the area of the culture is a measure of the number of bacteria present. Suppose that the area of the culture, A(t), in square millimeters, given by this function of time t, in hours: A(t)=9(1.1^t). Find the A(0), A(5) and A(10), the area at times t=0h, 5h, and 10h, respectively.

Answer 1

The equation for area of the bacteria culture at time t is given as:

$A(t)=9(1.1)^t$

So the values of A(0), A(5) and A(10) respectively, are:

$\begin{gathered} A(0)=9(1.1)^0=9 \\ A(5)=9(1.1)^5=14.49459\approx14.50 \\ A(10)=9(1.1)^{10}=23.34368\approx23.34 \end{gathered}$

Hence A(0)=9 sqmm, A(5)=14.4946sqmm, A(10)=23.3437 sqmm.