Question

Write an exponential function in the form y=abˣy=ab x that goes through points

(0,20) and (2,180).

Answer 1

The exponential function that goes through the points (0,20) and (2,180) is f(x) = 20 * 3^x.

Step-by-step explanation:

We're asked to write an exponential function of the form y=abx that passes through the points (0,20) and (2,180).

First, plug in the coordinates of the first point into the equation to find a:

• y=abx
• 20=a*b0
• 20=a*1
• a=20

Now that we have a, substitute a and the coordinates of the second point to solve for b:

• y=20bx
• 180=20b2
• 9=b2
• b=3 (since b>0 in exponential growth)

Finally, we combine a and b to get the exponential function:

f(x) = 20 * 3x