Final answer:
The calculation using the function p(3) = -9 + 30 + 50 = 71 indicates there should be 71 customers after 3 hours; however, the function's maximum is 86 customers, so options given in the question seem incorrect.
Step-by-step explanation:
The correct answer is option C) 86 customers. To determine how many customers are in the store 3 hours after it opens, we use the function p(t) = -t² + 10t + 50, where t represents time in hours. We substitute 3 for t to find p(3) = -(3)² + 10(3) + 50.
This simplifies to p(3) = -9 + 30 + 50 = 71 + 50 = 121. However, it seems we have made a mistake because p(t) will have a maximum value of 86 customers, occurring at the vertex of the parabola t = -b/(2a) from the quadratic formula. Since a is negative, this function opens downward meaning its maximum value happens at the vertex. Following our function, the vertex would occur at t = -10/(2*(-1)) = 5 hours. Hence, the number of customers can never exceed 86. Therefore, 121 customers is not obtainable with the given function. When recalculating properly for 3 hours after opening, we get p(3) = -(3)² + 10(3) + 50 = -9 + 30 + 50 = 71. So, there would be 71 customers after 3 hours, and the provided options are incorrect based on the given function.