the annual household cost of telephone service in the US increased at a relatively constant rate of $27.80 per year from 1981 to 2001. IN 2001 the annual household cost of telephone service was $914.
a:What was the annual household cost of telephone service in 1981?
B: Write an equation that gives the annual household cost of telephone service as a function of the number of year since 1981.
C: find the household cost of telephone service in 2000
cost at t years from 1981 is
c = x + 27.80t
to find the cost in 1981, just plug in c=914 and t=20 and solve for x.
The function is above. It's kind of stupid to ask for the cost in 2000 -- we know it's $27.80 less than in 2001! Should have asked for some other year, to make use of the formula.
a: To find the annual household cost of telephone service in 1981, we can use the information provided. We know that the annual household cost increased at a relatively constant rate of $27.80 per year from 1981 to 2001. In 2001, the annual household cost was $914. Therefore, we need to subtract 20 years (from 2001 to 1981) times the constant rate from the cost in 2001.
Calculation:
Annual household cost in 1981 = $914 - (20 years * $27.80)
Annual household cost in 1981 = $914 - $556
Therefore, the annual household cost of telephone service in 1981 was $358.
b: To write an equation that gives the annual household cost of telephone service as a function of the number of years since 1981, we can use the information provided. The annual household cost increased at a relatively constant rate of $27.80 per year from 1981.
Let C(t) be the annual household cost of telephone service in year t, where t is the number of years since 1981.
The equation for the annual household cost can be written as:
C(t) = C(1981) + (rate per year) * t
Since we know that C(1981) = $358 and the rate per year is $27.80, the equation becomes:
C(t) = $358 + ($27.80) * t
c: To find the household cost of telephone service in 2000, we need to calculate the number of years since 1981. Since 1981 is the starting point, we subtract 1981 from 2000 to find the number of years.
Calculation:
Number of years since 1981 = 2000 - 1981 = 19 years
Using the equation from part (b) with the calculated number of years, we get:
C(t) = $358 + ($27.80) * 19
C(t) = $358 + $529.20
Therefore, the household cost of telephone service in 2000 was $887.20.