Question

Write an exponential function for a graph that passes through the points (2, 336) and (3, 2688). Write the function in the form y = a(b). please I need help ​

Answer 1

y = 5.25
`(8)^(x)`

Explanation:

the general form of an exponential function is

y = a
`(b)^(x)`

to find a and b , substitute the coordinates of the given points into the equation.

using (2, 336 )

336 = a b² → (1)

using (3, 2688 )

2688 = a b³ → (2)

divide (2) by (1)

`(ab^3)/(ab^2)` =
`(2688)/(336)` ( cancel ab on numerator/denominator of left side )

b = 8

substitute b = 8 into (1) and solve for a

336 = a × 8² = 64a ( divide both sides by 64 )

5.25 = a

then exponential function is

y = 5.25
`(8)^(x)`