Question

HELP ASAP

write the equation of the exponential function y=ab^2

Answer 1

The exponential function is y =
`1600(1.25)^(x)`

Explanation:

The form of the exponential function is y = a
`b^(x)`, Where

• a is the initial value (value y at x = 0)

• b is the exponential factor

Let us use the form above to solve the question

→ From the given table

∵ At x = 0, y = 1600

∵ from the form above a is the value of y at x = 0

∴ a = 1600

→ Substitute it in the form of the equation above

∴ y = 1600
`(b)^(x)`

→ To find b use the point from the table and substitute x and y by its

coordinates

∵ At x = 1, y = 2000

→ Substitute them in the equation

∴ 2000 = 1600
`(b)^(1)`

∴ 2000 = 1600(b)

→ Divide both sides by 1600 to find b

∴ 1.25 = b

→ Substitute it in the equation

∴ y = 1600
`(1.25)^(x)`

∴ The exponential function is y =
`1600(1.25)^(x)`