Question

Write an exponential function in the form y=ab^xy=ab x that goes through points (0, 3)(0,3) and (4, 7203)(4,7203).

Answer 1

Answer:

$y = 3(7)^x$

Step-by-step explanation:

Given

$(x_1,y_1) = (0,3)$

$(x_2,y_2) = (4,7203)$

Required

Determine an exponential function

Substitute 0 for x and 3 for y in $y=ab^x$

$3 = ab^0$

$3 = a*1$

$3 = a$

$a = 3$

Substitute 4 for x and 7203 for y in $y=ab^x$

$7203= ab^4$

Substitute 3 for a

$7203= 3*b^4$

Divide both sides by 3

$2401= b^4$

Take 4th root of both sides

$\sqrt[4]{2401} = b$

$7 = b$

$b = 7$

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

$y = 3(7)^x$