Question

write the equation for an exponential function, in the form axb^x, whose graph passes through the coordinates points (1, 7.5) ( 3, 16.875)

Answer 1

see explanation

Explanation:

The equation of the exponential function in the form

y = a
`b^(x)`

Substitute the given points into the equation and solve for a and b

Using (1, 7.5), then

7.5 = ab → (1)

Using (3, 16.875), then

16.875 = ab³ → (2)

Divide (2) by (1)

`(ab^3)/(ab)` =
`(16.875)/(7.5)`, hence

b² = 2.25 ( take the square root of both sides )

b = 1.5

Substitute b = 1.5 into (1)

1.5a = 7.5 ⇒ a = 5

The exponential function is y = 5
`(1.5)^(x)`