Question

Find the equation of the exponential function represented by the table below:

Answer 1

Answer:

$y =5(3)^x$

Step-by-step explanation:

Given

The attached table

Required

Determine the equation of the table

The table represents an exponential function. So, we make use of

$y = ab^x$

When x = 0, y= 5.

So:

$y = ab^x$ becomes

$5 = ab^0$

$5 = a*1$

$5 = a$

$a = 5$

When x = 1; y = 15

So;

$y = ab^x$ becomes

$15 = a * b^1$

$15 = a * b$

Substitute 5 for a

$15 = 5 * b$

Divide both sides by 5

$\frac{15}{5} = \frac{5 * b}{5}$

$3 = b$

$b = 3$

Substitute values for a and b in: $y = ab^x$

$y =5(3)^x$