Question

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Answer 1

Given the function:

`b(t)=100\cdot2^t`

This function represents an exponential growth.

Take the exponential growth function:

`\begin{gathered} f(x)=a\cdot b^x \\ \\ \text{Where a represents the initial amount} \\ b\text{ represnts the growth rate} \\ x\text{ represents the exponent} \end{gathered}`

In an exponential function, the quantity increases slowly at first, then increases rapidly in the later stages.

The function above models an experiment in a science class where the experiment is started with 100 bacteria, then doubles every hour.

From the function, we have the following:

`b(t)=100\cdot2^t`

The variable t represent the number of hours since the experiment began

The b(t) represents the number of cells in the bacteria population

ANSWER:

• Hours since the experiment began

• Cells in the bacteria population