Question

Use the table to answer the 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.
f(4)=(_)

Answer 1

Annabel wants to make banana bread for the bake sale. She went to the market to buy bananas, and she noticed fruit flies after she returned home with her produce. The number of fruit flies grows at an exponential rate modeled by the equation f(t)=8(2)^t
, where f is the number of fruit flies after t days. Define an appropriate domain for the problem if Annabel bakes the banana bread 5 days after returning from the market.(1 point)
Responses

0≤t≤5
0 less than or equal to t less than or equal to 5

0≤t≤256
0 less than or equal to t less than or equal to 256

0≤f≤5
0 less than or equal to f less than or equal to 5

0≤f≤256
0 less than or equal to f less than or equal to 256

Answer 2

To find the missing value \( f(4) \) in the table for the function \( f(x) = 3(1.2)^x \), we can substitute \( x = 4 \) into the function.

\[
f(4) = 3(1.2)^4
\]

Now, let's 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, substitute back into the function:

\[
f(4) = 3 \times 2.0736 = 6.2208
\]

Finally, rounding this value to two decimal places gives:

\[
f(4) \approx 6.22
\]

So, the missing value in the table is:

\[
f(4) = 6.22
\]

Answer 3

Given the context that Annabel will be baking banana bread 5 days after returning from the market, the appropriate domain for the number of days \( t \) is:

\[
0 \leq t \leq 5
\]

This indicates that \( t \) starts at 0 days (when she returns from the market) and goes up to 5 days (the day she bakes the banana bread).

Thus, the correct response is:

**0 ≤ t ≤ 5**