Question

The table shows the annual visitors to a museum in millions. Write an equation for the projected number of visitors after n years.

Answer 1

The table of values is an illustration of an exponential function

The equation for the projected number of visitors after n years is $a_n = 4 * 1.5^{n - 1}$

How to determine the equation

An exponential function is represented as:

$y = ab^x$

From the table, we have:

(x,y) = (1,4) and (2,6)

So, we have:

$y = ab^x$

$ab^1 = 4$

$ab =4$

Also, we have:

$ab^2 = 6$

Divide both equations

$ab^2 \div ab = 6 \div 4$

$b = 1.5$

Substitute 1.5 for b in ab = 4

So, we have:

$1.5a = 4$

Divide through by 1.5

$a = \frac{4}{1.5}$

Recall that:

$y = ab^x$

So, we have:

$y = \frac 4{1.5} * 1.5^x$

This gives

$y = 4 * 1.5^{x - 1}$

Rewrite as:

$a_n = 4 * 1.5^{n - 1}$

Hence, the equation for the projected number of visitors after n years is $a_n = 4 * 1.5^{n - 1}$

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