Question

The exponential function h, represented in the table, can be written as h(x) = a.2.

2
h(s)
0
10
1
4
Complete the equation for h(c).
h(z) =
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Answer 1

h(x) = 10
`(0.4)^(x)`

Explanation:

The exponential is of the form

h(x) = a
`(b)^(x)`

Use the ordered pairs from the table to find a and b

Using (0, 10 ), then

10 = a
`b^(0)` (
`b^(0)` - 1 ), thus

a = 10

h(x) = 10
`b^(x)`

Using (1, 4 ), then

4 = 10
`b^(1)` , hence

b =
`(4)/(10)` = 0.4

h(x) = 10
`(0.4)^(x)`