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$Write an exponential function to model the situation. Then solve. The cost of tuition at a college is $12,000 and is increasing at a rate of 6% per year. What will the cost be after 4 years? {:[C(t)=12000(1.06)^(t)"; "],[C(t)=12000(.06)^(t)"; "],[C(t)=12000(.06)^(t)"; "],[C(t)=12000(1.06)^(t)"; "],[$3149.72],[$1472.95],[$3149.72]:}$

Write an exponential function to model the situation. Then solve. $\newline$ The cost of tuition at a college is $\$ 12,000$ and is increasing at a rate of $6 \%$ per year. What will the cost be after $4$ years? $\newline$ $\begin{array}{l} C(t)=12000(1.06)^{t} \text {; } \\ C(t)=12000(.06)^{t} \text {; } \\ C(t)=12000(.06)^{t} \text {; } \\ C(t)=12000(1.06)^{t} \text {; } \\ \$ 3149.72 \\ \$ 1472.95 \\ \$ 3149.72 \\ \end{array}$

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Math Problems

Algebra 1

Write linear and exponential functions: word problems

Full solution

Q. Write an exponential function to model the situation. Then solve.

\newline

The cost of tuition at a college is

\$ 12,000

and is increasing at a rate of

6 \%

per year. What will the cost be after

4

years?

\newline

\begin{array}{l} C(t)=12000(1.06)^{t} \text {; } \\ C(t)=12000(.06)^{t} \text {; } \\ C(t)=12000(.06)^{t} \text {; } \\ C(t)=12000(1.06)^{t} \text {; } \\ \$ 3149.72 \\ \$ 1472.95 \\ \$ 3149.72 \\ \end{array}

Identify Function Type: Identify the type of function to model the situation. $\newline$ Since the cost of tuition is increasing at a percentage rate per year, this is an exponential growth situation.
Write Exponential Function: Write the exponential function to model the situation. $\newline$ The general form of an exponential growth function is $C(t) = a(1 + r)^t$ , where: $\newline$ - $C(t)$ is the cost after $t$ years, $\newline$ - $a$ is the initial amount, $\newline$ - $r$ is the growth rate (expressed as a decimal), $\newline$ - $t$ is the time in years. $\newline$ Given $a = \$12,000$ and $r = 6\%$ or $0.06$ , the function is $C(t) = 12000(1.06)^t$ .
Calculate Tuition Cost: Calculate the cost of tuition after $4$ years. $\newline$ Substitute $t = 4$ into the function $C(t) = 12000(1.06)^t$ to find $C(4)$ . $\newline$ $C(4) = 12000(1.06)^4$
Perform Calculation: Perform the calculation for $C(4)$ . $C(4) = 12000(1.06)^4$ $C(4) = 12000 \times (1.262476)$ $C(4) = 15149.712$
Round to Nearest Cent: Round the result to the nearest cent, if necessary. $\newline$ The cost of tuition after $4$ years is $\$15,149.71$ when rounded to the nearest cent.