Question

Costs for a campground are $60 for

1 night, and $150 for 3 nights. Assuming
that the costs increase linearly, which
equation shows the costs, c, for n nights?

Choices:
A. c = 15n + 45
B. c = 45n + 15
C. c = 60n + 150
D. c = 180n

Answer 1

Answer: Option B

Explanation:

$60 per 1 night

$150 per 3 nights

If this is a linear c(n) function, que can obtain the slope by:

s = (c2 - c1)/(n2 - n1)

where c2 = c(n2) and c1 = c(n1)

in this case y is the price and n is the number of nights.

s = ($150 - $60)/(3 - 1) = $90/2 = $45

Then c(n) = $45*c + b

we know that c(1) = $60 = $45*1 + b

b = $60 - $45 = $15

then the linear equation is:

c(n) = $45*n + $15

Answer 2

Replace n in the equations with 1 and then 3 and see which one will equal 60 for 1 night and 150 for 3 nights.

The equation that works is B. c = 45n +15