Could someone answer this question so I understand it. Thanks
Find the supply function:
p = S(x)=5(e^0.02x - 1)
Find the average price (in dollars)over the supply interval [31,36]. Round to decimal places as needed.
The average price in dollars is ?
To find the average price over the supply interval [31,36], we need to calculate the average value of the supply function within that interval.
Step 1: Substitute the values 31 and 36 into the supply function.
p = S(x) = 5(e^(0.02x) - 1)
p(31) = 5(e^(0.02 * 31) - 1)
p(36) = 5(e^(0.02 * 36) - 1)
Step 2: Calculate the average price using the formula:
Average price = (p(31) + p(36)) / 2
Step 3: Plug in the values of p(31) and p(36) into the formula and perform the calculations.
Average price = (5(e^(0.02 * 31) - 1) + 5(e^(0.02 * 36) - 1)) / 2
To determine the actual value of the average price in dollars, you would need to evaluate this expression using a calculator or software that can handle exponential functions and then round the result to the desired number of decimal places.