Use the table to answer the question.

Question

x f(x)

0 3
1 3.6
2 4.32
3 5.18
4 ?

5 7.46
Find the missing value in the table for the exponential function f(x)=3(1.2)x
. Round your answer to two decimal places.

(1 point)

Answer 1

To find the missing value of $f(x)$ for $x=4$ using the given exponential function $f(x)=3(1.2{)}^x$, we can substitute $x=4$ into the function.

Calculating $f(4)$:

$$f(4)=3(1.2{)}^4$$

Now, calculate $(1.2{)}^4$:

$$(1.2{)}^4=1.2\times 1.2\times 1.2\times 1.2$$

Calculating step-by-step:

1. $1.2\times 1.2=1.44$
2. $1.44\times 1.2=1.728$
3. $1.728\times 1.2=2.0736$

Now plug this back into the equation:

$$f(4)=3\times 2.0736=6.2208$$

Rounding to two decimal places:

$$f(4)\approx 6.22$$

Thus, the missing value in the table for $x=4$ is:

$$\boxed{{\displaystyle 6.22}}$$