Question

the equation c = 84t + 1923 can be used to estimate the average cost of tuition and fees at two - year public institutions of higher education, where t is the number of years since 2005.
a) what was the average cost of tuition and fees in 2007? in 2012?
b) for what years will the cost of tuition and fees be more than $2500?
a) in 2007, the average cost of tuition and fees was $2091. (round to the nearest whole number.)
in 2012, the average cost of tuition and fees was $2511. (round to the nearest whole number.)
b) select the correct choice below and fill in the answer box to complete your choice. (simplify your answer. type an integer or a decimal rounded to two decimal places as needed.)
a. before years, the cost of tuition and fees will be more than $2500.
b. after years, the cost of tuition and fees will be more than $2500.

Explanation:

Step1: Calculate t for 2007

Find the number of years since 2005. $t = 2007 - 2005=2$.

Step2: Calculate cost for 2007

Substitute $t = 2$ into $C = 84t+1923$. $C=84\times2 + 1923=168+1923 = 2091$.

Step3: Calculate t for 2012

Find the number of years since 2005. $t = 2012 - 2005 = 7$.

Step4: Calculate cost for 2012

Substitute $t = 7$ into $C = 84t+1923$. $C=84\times7+1923=588 + 1923=2511$.

Step5: Solve for t when $C>2500$

Set up the inequality $84t + 1923>2500$.
Subtract 1923 from both sides: $84t>2500 - 1923$, so $84t>577$.
Divide both sides by 84: $t>\frac{577}{84}\approx6.87$.
Since $t$ represents years since 2005, the year is $2005 + 7=2012$ (rounding up $t$ to the next whole - year).

Answer:

a) In 2007, the average cost of tuition and fees was $\$2091$. In 2012, the average cost of tuition and fees was $\$2511$.
b) B. After 6.87 years, the cost of tuition and fees will be more than $\$2500$.