Question

ponential functions
which graph is the sequence defined by the function $f(x) = 3(2)^{x - 1}$?
(there are graphs with points: first graph has (1,3), (2,6), (3,12), (4,24), (5,48); second has (0,2), (1,6), (2,18), (3,54), (4,162); third has (1,2), (2,6), (3,18), (4,54), (5,162); and a partial fourth graph.)
mark and return
17 of 25
save & exit

Explanation:

Step1: Calculate f(1)

Substitute \( x = 1 \) into \( f(x)=3(2)^{x - 1} \).
\( f(1)=3(2)^{1 - 1}=3(2)^{0}=3\times1 = 3 \).

Step2: Calculate f(2)

Substitute \( x = 2 \) into \( f(x)=3(2)^{x - 1} \).
\( f(2)=3(2)^{2 - 1}=3(2)^{1}=3\times2 = 6 \).

Step3: Calculate f(3)

Substitute \( x = 3 \) into \( f(x)=3(2)^{x - 1} \).
\( f(3)=3(2)^{3 - 1}=3(2)^{2}=3\times4 = 12 \).

Step4: Calculate f(4)

Substitute \( x = 4 \) into \( f(x)=3(2)^{x - 1} \).
\( f(4)=3(2)^{4 - 1}=3(2)^{3}=3\times8 = 24 \).

Step5: Calculate f(5)

Substitute \( x = 5 \) into \( f(x)=3(2)^{x - 1} \).
\( f(5)=3(2)^{5 - 1}=3(2)^{4}=3\times16 = 48 \).

Now, check the graphs. The first graph has points \((1, 3)\), \((2, 6)\), \((3, 12)\), \((4, 24)\), \((5, 48)\), which match the calculated values.

Answer:

The Left Graph (the first graph with points (1,3), (2,6), (3,12), (4,24), (5,48))