Question

1. determine the explicit rule in function notation for the arithmetic sequence. below is a table for the cost of electricity in kwh from an electric company. use the table to answer problems a – c.

a. what is the common difference of the sequence represented in the table? select one.
$9.00
$0.90
$0.09
b. what is the explicit rule for the sequence? select one.
f(n) = 0.09n
f(n) = 0.09n + 5.00
f(n) = 0.09n + 5.45
c. find the cost of using 50 kwh of electricity. select one.
$4.50
$9.50
$18.00

Explanation:

Step1: Calculate common difference

Subtract consecutive costs: $5.54 - 5.45 = 0.09$, $5.63 - 5.54 = 0.09$

Step2: Identify explicit rule

Arithmetic sequence: $f(n) = f(1) + d(n-1)$. $f(5)=5.45$, so $5.45 = f(1) + 0.09(5-1) \Rightarrow f(1)=5.45 - 0.36=5.09$? No, wait: $f(n)=5.00 + 0.09n$? Check $n=5$: $5+0.45=5.45$ (matches); $n=6$: $5+0.54=5.54$ (matches); $n=7$: $5+0.63=5.63$ (matches). Correct.

Step3: Compute cost for 50 kWh

Use $f(n)=5.00 + 0.09n$. $n=50$: $5 + 0.09×50=5 + 4.5=9.50$

Answer:

a. $0.09$
b. $f(n)=0.09n + 5.00$
c. $9.50$