Question

question 4 (multiple choice worth 2 points) (05.05r mc) a table of data is given.

x	f(x)
-2	71
-1	13
0	3
1	0.6
2	0.1

which exponential model best represents the data?

• f(x) = 3(1.2)^x
• f(x) = 2(0.3)^x
• f(x) = 2(3)^x
• f(x) = 3(0.2)^x

Explanation:

Step1: Recall exponential form

The general exponential model is $f(x)=ab^x$, where $a=f(0)$.

Step2: Find $a$ from the table

When $x=0$, $f(0)=3$, so $a=3$. This eliminates options with $a=2$.

Step3: Test remaining options with $x=1$

For $f(x)=3(1.2)^x$: $f(1)=3(1.2)=3.6$, which does not match the table's $f(1)=0.6$.
For $f(x)=3(0.2)^x$: $f(1)=3(0.2)=0.6$, which matches the table.

Step4: Verify with another $x$-value

Test $x=2$ for $f(x)=3(0.2)^x$: $f(2)=3(0.2)^2=3(0.04)=0.12\approx0.1$, which matches the table.

Answer:

D. $f(x)=3(0.2)^x$