Question

Find the formula for an exponential function that passes through the two points given.

Answer 1

Answer:

$y = 7(3^x)$

Step-by-step explanation:

Given

$(x_1,y_1) = (0,7)$

$(x_2,y_2) = (4,567)$

Required

Determine the formula

An exponential function is of the form:

$y = ab^x$

For point $(x_1,y_1) = (0,7)$

$7 = ab^0$

$7 = a*1$

$7 = a$

$a = 7$

For point $(x_2,y_2) = (4,567)$

$567 = ab^4$

Substitute 7 for a

$567 = 7*b^4$

Divide both sides by 7

$81 = b^4$

Take 4th root of both sides

$\sqrt[4]{81} =\sqrt[4]{b^4}$

$\sqrt[4]{81} =b$

$b = \sqrt[4]{81}$

$b = 3$

Substitute 7 for a and 3 for b in $y = ab^x$

$y = 7 * 3^x$

$y = 7(3^x)$