Question

Use the graph to write an explicit function to represent the data and determine how much money Taryn earned in week 5.

graph with x axis labeled Number of Weeks and ranges from zero to seven, y axis labeled Money Earned, in dollars, and ranges from zero to one hundred eighty with points at one comma four, two comma twelve, three comma thirty six, and four comma one hundred eight

f(n) = (3)n − 1; f(5) = 81
f(n) = 4(3)n + 1; f(5) = 2,916
f(n) = 4(3)n; f(5) = 972
f(n) = 4(3)n − 1; f(5) = 324

Answer 1

Answer:

answer is C f(n) = 4(3)n; f(5) = 972

Step-by-step explanation:

i took the test, also

Answer 2

The graph is an illustration of an exponential function

The true statement is (d) $\mathbf{f(n) = 4(3)^{n-1}}$, $\mathbf{f(5) = 324}$

An exponential function is represented as:

$y = ab^{x-1}$

From the graph, we have the following points

$(x_1,y_1) = (1,4)$

$(x_2,y_2) = (2,12)$

So, we have:

$y = ab^{x-1}$ --------- $(x_1,y_1) = (1,4)$

$4 = ab^{1-1}$

$4 =ab^0$

$4 =a \times 1$

$4 =a$

$a = 4$

$y = ab^{x-1}$ --------- $(x_2,y_2) = (2,12)$

$12 = ab^{2-1$

$12 = ab$

Substitute $a = 4$

$12 = 4b$

Divide both sides by 4

$3 = b$

$b =3$

Recall that:

$y = ab^{x-1}$

So, we have::

$y = 4(3)^{x-1}$

Express as a function of n

$\mathbf{f(n) = 4(3)^{n-1}}$

Substitute 5 for n, to calculate the 5th term

$\mathbf{f(5) = 4(3)^{5-1}}$

$\mathbf{f(5) = 4(3)^4}$

$\mathbf{f(5) = 324}$

Hence, option (d) is correct

Read more about exponential functions as:

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