Question

Call centers are booming in a country as multinational companies increasingly outsource these operations. The annual revenue for call centers in the country from 2006 to 2010, in billions of dollars, can be modeled by:

R(x) = 0.945x - 3.16, where x is the number of years after 2000.
a. According to the model, what was the rate of change of revenue for call centers in the country?
b. According to the model, what was the revenue for call centers in the country in 2010?
c. Would this model be valid to estimate the revenue in 2000? Why or why not?
d. According to the model, the rate of change of revenue for call centers in the country was $____ billion per year.

Answer 1

The model indicates a rate of change of $0.945 billion per year for call center revenue. Revenue in 2010 was $6.29 billion. The model isn't valid for estimating 2000 revenue as it would yield a negative value.

Step-by-step explanation:

The rate of change of revenue for call centers in the country, according to the model, is represented by the coefficient of x in the equation R(x) = 0.945x - 3.16. This means the rate of change is $0.945 billion per year.

To calculate the revenue for call centers in 2010, we substitute x with 10 (since 2010 is 10 years after 2000) into the equation, resulting in R(10) = 0.945(10) - 3.16, which calculates to $6.29 billion.

The model would not be valid to estimate the revenue in 2000 because when x is 0, the revenue model gives a negative value, which is not feasible for revenue amounts. Additionally, the model appears to only be calibrated for data from 2006 onwards and may not accurately reflect conditions prior to this period.

Summing up, the rate of change of revenue according to the model is $0.945 billion per year.