Question

Find the equation of the exponential function, in y=a(b)^x form that passes through the points (-2,3) and (6,35). Round both a and b to the nearest hundredth. Must be an algebraic method.

Answer 1

I supose your function is: $y(x)=a \cdot b^x$

Step 1. Replace the coordinates of the first point in your equation:
x=-2, y=3

$3=a \cdot b^{-2}$

Solve the equation for "a":
$a=3 \cdot b^2$

Step 2. Replace the coordinates of the second point in your equation:
x=6, y=35

$35 = a \cdot b^6$

Replace the value of "a" from Step 1.
$35 = 3 \cdot b^2 \cdot b^6$
Calculate "b":
$b= \sqrt[8]{\frac{35}{3}} = 1.359466$

Step 3. Replace "b" in first equation and calculate "a":
$a=3 \cdot b^2=5.5444434$

The equation is:
$y(x)=5.54 \cdot 1.36^x$