Question

Find the equation of the exponential function represented by the table below:

y=

Answer 1

The value of exponential function: y = 0.2(0.5)ˣ

Explanation:

We know that the exponential function is of the form

y = abˣ

From the table, it is clear that

when x = 0, y = 0.2

so substitute x = 0, y = 0.2

`0.2\:=\:ab^(0)`

0.2 = a × 1 ∵ b⁰ = 1

0.2 = a

so, we have a = 0.2

now substitute x = 1 and y = 0.1

y = abˣ

0.1 = 0.2×b¹

0.1 = 0.2×b

b = 0.1/0.2

b = 0.5

now substituting a = 0.2 and b = 0.5

y = abˣ

y = 0.2(0.5)ˣ

Therefore, the value of exponential function: y = 0.2(0.5)ˣ