Question

The sketch below shows a graph with the equation y=ab^x

Work out the values of a and b

Answer 1

The values of a and b are,

a = 5, b = 3

Explanation:

We are given that (1,15) , and (4,405) are on the graph of the equation

y = ab^x

so,

15 = ab^(1) (i)

405 = ab^(4) (ii)

solving this system of equations,

dividing (ii) by (i),

405/15 = ab^(4)/ab

27 = b^(4-1)

27 = b^3

taking the cube root,

`b = \sqrt[3]{27}\\ b = 3`

b = 3

Putting this value in (i),

15 = a(3)

a = 15/3

a = 5

Hence a = 5, b = 3

Answer 2

Answer:

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