Question

The sketch below shows part of the graph of y = ab",

where a and b are constants.
YA
(0,8)
Work out the values of a, b and k.
(1.5, k)
(1, 18)

Answer 1

Correct Answer:

a = 8
b = 2.25
k = 27

Answer 2

y = 8*(9/4)^x

Point (1.5, 27)

Explanation:

We can solve each unknown in separate steps. The first step is to take advantage of given point (0,8) to find the value of a. Since x is zero, b^x will just be 1, regardless of b. That makes it easy to solve for a, which is found to be 8.

Once a is known, we can use the next point (1,18) to solve for b. b is (9/4).

Once we have a and b, we have the full equation: y = 8*(9/4)^x

k is found by entering the x value and solving for y (which is k). k = 27

See attached worksheet