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 years since 1981.
c: find the household cost of telephone service 2000
a. X + 27.80*20 = 914
X = $358.
b. C = 358 + 27.80x
X = The number of years since 1981.
c. 2000-1981 = 19 years.
C = 358 + 17.80*19 = $528.20
a: To find the annual household cost of telephone service in 1981, we need to subtract the total increase from the 2001 cost.
Cost in 1981 = 2001 cost - total increase
Cost in 1981 = $914 - ($27.80 * (2001 - 1981))
Cost in 1981 = $914 - ($27.80 * 20)
Calculating the result, the annual household cost of telephone service in 1981 was $544.
b: The equation that gives the annual household cost of telephone service as a function of the number of years since 1981 is:
Cost = Initial cost + (Rate per year * (Current year - 1981))
c: To find the household cost of telephone service in 2000, we need to substitute the year 2000 into the equation:
Cost in 2000 = Initial cost + (Rate per year * (2000 - 1981))
Cost in 2000 = $544 + ($27.80 * (2000 - 1981))
Calculating the result, the household cost of telephone service in 2000 was $841.
To answer these questions, we need to understand the given information and use it to determine the annual household cost of telephone service in different years.
a. To find the annual household cost of telephone service in 1981, we need to determine the initial cost before the increase. According to the information provided, the annual household cost increased at a constant rate of $27.80 per year. Therefore, to find the cost in 1981, we subtract the total increase from the cost in 2001.
Cost in 2001 = $914
Total increase from 1981 to 2001 = $27.80 per year * (2001 - 1981)
So, the annual household cost in 1981 can be calculated as:
Cost in 1981 = Cost in 2001 - Total increase
Cost in 1981 = $914 - ($27.80 * (2001 - 1981))
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 need to consider the constant rate of increase. Let's take "y" as the number of years since 1981, and "C(y)" as the annual household cost.
Based on the given information, the cost increases at a rate of $27.80 per year from 1981. So, the equation can be written as:
C(y) = Initial cost + Rate of increase per year * y
In this case:
Initial cost = Cost in 1981
Rate of increase per year = $27.80
Therefore, the equation becomes:
C(y) = Cost in 1981 + $27.80 * y
c. To find the household cost of telephone service in 2000, we need to determine the number of years since 1981. Since we're looking for the cost in 2000, that would be 2000 - 1981 = 19 years.
Using the equation from part b, we can substitute "y" with 19 to find the household cost in 2000:
C(19) = Cost in 1981 + $27.80 * 19