Question

Sam wants to create a linear function and an exponential function, both of which have a y-intercept

of (0,8) and pass through the point (9,512). Help Sam create his functions.

Answer 1

Explanation:

Exponential function is

`y = a * {b}^(x)`

where a is the y intercept, or the initial value.

b is the constant rate.

Since a is the y intercept, this means a is 8. So we have

`y = 8 * {b}^(x)`

Now, plug in 9 for x. 512 for y to find b.

`512 = 8 * {b}^(9)`

`64 = {b}^(9)`

`\sqrt[9]{64} = b`

`64 {}^{ (1)/(9) } = b`

`4 {}^{ (1)/(3) } = b`

`\sqrt[3]{4} = b`

So the equation is

`y = 8( \sqrt[3]{4} ) {}^(x)`