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

Step-by-step explanation:

Exponential function is

$y = a \times {b}^{x}$

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

$y = 8 \times {b}^{x}$

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

$512 = 8 \times {b}^{9}$

$64 = {b}^{9}$

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

$64 {}^{ \frac{1}{9} } = b$

$4 {}^{ \frac{1}{3} } = b$

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

So the equation is

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