Exponential from Two Points

Question

Write an exponential function in the form y=ab^x that goes through points (0,14) and (3,896).

Answer 1

(0,14) tells you that when x = 0, y = 14.

So:

14 = a(b)⁰ (or a = 14).

At this point we have y = 14b^x.

(3, 896) tells you that when x = 3, y = 896.

896 = 14(b)³

How to solve for b?

Divide both sides by 14 for starters:

64 = b³

Now take the cube root of both sides (or raise both sides to the 1/3 power).

64^1/3 = (b³)^1/3

b= 4.

So we have:

y = 14(4)^x

Check it out:

desmos.com/calculator/jhizblwurl