Question

Using the table of values, please write an exponential function that would best model this data.

Answer 1

`\textsf{A.} \quad y=2^x`

Explanation:

From inspection of the given table, we can see that the number of new infections is twice the number of infections recorded for the previous day. Therefore, we can use the exponential function formula to write a function that models the given data.

`\boxed{\begin{minipage}{9 cm}\underline{General form of an Exponential Function}\\\\$y=ab^x$\\\\where:\\\phantom{ww}$\bullet$ $a$ is the initial value ($y$-intercept). \\ \phantom{ww}$\bullet$ $b$ is the base (growth/decay factor) in decimal form.\\\end{minipage}}`

The initial value is the number of new infections on day 0:

• a = 1

The growth factor is 2, since the number of new infections doubles each day:

• b = 2

Substitute the values of a and b into the formula:

`y=1 \cdot 2^x`

`y=2^x`

Therefore, the exponential function that models the data is:

`\boxed{y=2^x}`