CPM Homework Help : A2C Problem 3-122

Find the equation of an exponential function that passes through the points $\left(2, 48\right)$ and $\left(5, 750\right)$ .

Step 1:

Substitute the values for $x$ and $y$ .

$y = ab^{x}$

$750 = ab^{5}$

$48=ab^2$

Step 2:

Solve both equation for $a$ .

$a=\frac{48}{b^{2}}$

$a=\frac{750}{b^{5}}$

Step 3:

Set the equations equal to each other. Solve for b by multiplying both sides of the equation by $b^{5}$ .

Step 4:

Substitute $b$ into one of the equations from Step 1 and solve for $a$ . After you know $a$ and $b$ , write the equation.

Answer:

$y = 7.68\left(2.5\right)^{x}$