Question

At noon, to begin a study, a petri dish had 2000 bacteria cellsEach hour since, the number of cells has increased by 15% Let be the number of hours since the start of the studyLet y be the number of bacteria cells Write an exponential function showing the relationship between y and

Answer 1

If the number of bacteria increases by 15% each hour, that means the previous value is multiplied by 1.15 for each increment of t.

We can model this situation using the following exponential equation:

$y=A\cdot(1+r)^t$

Where A is the initial value (for t = 0) and r is the growth or decay rate.

So, using A = 2000 and r = 0.15 (that is, 15%), we have:

$\begin{gathered} y=2000(1+0.15)^t\\ \\ y=2000(1.15)^t \end{gathered}$