Question

a researcher is curious about the spread of the spanish flu in 1918. a page from a records book from a hospital contained the following table. this table will allow the researcher to predict how many patients would have contracted the spanish flue by day 100. determine the exponential equation for the given table.

Explanation:

Step1: Recall the exponential equation form

The general form of an exponential equation is \(y = a\cdot b^{x}\), where \(a\) is the initial value and \(b\) is the base.

Step2: Find the initial value \(a\)

When \(x = 0\) (days), \(y=1\) (infected). Substituting into \(y = a\cdot b^{x}\), we get \(1=a\cdot b^{0}\). Since \(b^{0}=1\) for \(b
eq0\), then \(a = 1\).

Step3: Find the base \(b\)

We can use another pair of values. For example, when \(x = 1\), \(y = 3\). Substitute \(a = 1\) into \(y=a\cdot b^{x}\), we have \(3=1\cdot b^{1}\), so \(b = 3\).

Answer:

\(y = 3^{x}\)