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.

Question

asked Jun 23, 2023 40.2k views

1 Answer

Karisma · Answer 1 · 2023-06-27T01:27:58+0000

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

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