Question

A 2-column table has 5 rows. The first column is labeled x with entries negative 2, negative 1, 0, 1, 2. The second column is labeled f (x) with entries 12.5, 2.5, 0.5, 0.1, 0.02.

Which exponential function is represented by the table?

f(x) = 0.2(0.5x)
f(x) = 0.5(5x)
f(x) = 0.5(0.2x)
f(x) = 0.2(0.2x)

Answer 1

C.

Explaination:

I took the test

Answer 2

`f(x)=0.5\cdot (0.2)^x`

Explanation:

Given the table

`\begin{array}{cc}x&f(x)\\ \\-2&12.5\\ -1&2.5\\0&0.5\\1&0.1\\2&0.02\end{array}`

The exponential function can be written
`f(x)=a\cdot b^x.` To find
`a` and
`b,` substitute some values:

When
`x=0,\ f(x)=0.5,` then

`0.5=a\cdot b^0\Rightarrow a=0.5\ [ b^0=1]`

When
`x=1,\ f(x)=0.1,` then

`0.1=0.5\cdot b^1\Rightarrow 0.5b=0.1,\ b=0.2`

Thus,

`f(x)=0.5\cdot (0.2)^x`

Check remaining values:

`f(-2)=0.5\cdot 0.02^(-2)=0.5\cdot 5^2=0.5\cdot 25=12.5\\ \\f(-1)=0.5\cdot 0.2^(-1)=0.5\cdot 5=2.5\\ \\f(2)=0.5\cdot 0.2^2=0.5\cdot 0.04=0.02`