Question

Let 1995 correspond to x=0. Let b be the ratio between the population in 1995 and 1996. Determine an exponential function of the form y=a(b)^x to represent the population symbolically. Round to 3 decimal places.

Answer 1

The table is an illustration of an exponential function

The equation of the table is $y = 148 * 0.997^x$

How to determine the equation of the table

Given that 1995 corresponds to x = 0, then

The initial value (a) of the function is:

a = 148.0

The equation of the function is:

$y = ab^x$

When x= 1, we have:

$147.6 = ab^1$

$147.6 = ab$

This gives

$147.6 = 148b$

Divide both sides by 148

$b = 0.997$

Hence, the equation of the table is:

$y = 148 * 0.997^x$

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