Question

a concert has been sold out for weeks, and as the date of the concert draws closer, the price of the tickets increase. the cost of a pair of tickets was worth $131 four days ago and is $193 today. assume the cost continues to increase at a constant rate.

write an equation that could be used to find the daily rate of increase.

to the nearest percent, what is the daily rate of increase?
%

Explanation:

Step1: Define variables and growth model

Let $r$ = daily rate (decimal), $P_0=131$, $P=193$, $t=4$.
Exponential growth formula: $P = P_0(1+r)^t$
Substitute values: $193 = 131(1+r)^4$

Step2: Isolate the exponential term

Divide both sides by 131:
$\frac{193}{131} = (1+r)^4$

Step3: Solve for $(1+r)$

Take 4th root of both sides:
$1+r = \sqrt[4]{\frac{193}{131}}$

Step4: Calculate daily rate (decimal)

Compute $\sqrt[4]{\frac{193}{131}} \approx \sqrt[4]{1.4733} \approx 1.101$
Subtract 1: $r \approx 1.101 - 1 = 0.101$

Step5: Convert to percentage

Multiply by 100: $r \approx 0.101 \times 100 = 10.1\%$, rounded to 10%

Answer:

Equation: $\boldsymbol{193 = 131(1+r)^4}$
Daily rate of increase: $\boldsymbol{10\%}$