We need to construct an explicit rule in function notation for the arithmetic sequence represented in the table. Then we will find and interpret the meaning of $f (18)$ in the given context.

Number of battery packs	$n$	$1$	$2$	$3$	$4$
Total cost ( $$$ )	$f (n)$	$4.90$	$8.90$	$12.90$	$16.90$

f (n)

represents the total cost, in dollars, of purchasing

n

battery packs. Since we are dealing with an arithmetic sequence, we can describe it using the general explicit rule.

f (n) = f (1) + d (n - 1)

Notice that, in this case,

f (1) = 4.90 .

The next thing we need to do is to find the common difference

d .

This can be done by finding the difference of any two consecutive terms.

d = f (2) - f (1) = 8.90 - 4.90 = 4

We can now substitute the obtained values in the general explicit rule.

f (n) = 4.90 + 4 (n - 1)

Finally, to find

f (18),

we will substitute

18

for

n

in the above formula.

f (n) = 4.90 + 4 (n - 1)

Substitute

$n = 18$

f (18) = 4.90 + 4 (18 - 1)

SubTerm

Subtract term

f (18) = 4.90 + 4 (17)

Multiply

f (18) = 4.90 + 68

AddTerms

Add terms

f (10) = 72.90

We found that

f (18) = 72.90 .

In the given context, this means that purchasing

18

battery packs costs

$ 72.90 .

Exercise

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