The profit from the supply of a certain commodity is modeled as 76qe 0.5q dollars P(q) where q is the number of units produced. 0 sq 100 (a) Write an expression for the rate of change of profit. dollars per unit P'(q) (b) At what production level in the domain 0 s q s 100 is the rate of change of profit zero? (Round your answer to the nearest whole number.) units q (c) What is profit at the production level found in part (b)? (Round your answer to two decimal places.) $

Plot the function ?(?) =1/X

Graph the functions in excercise

The amount of money in a savings account after tyears is represented by the function(t) = 500(1.015)'. What does the value 500 represent in the situation? The amount of money in the savings account decreases by $500 each year. The amount of money in the savings account is 500 times the amount of the previous year. The initial amount in the account is $500. O The amount of money in the savings account increases by $500 each year.

Use function notation to represent the change in Sam's height above the ground over the time interval from t=4 seconds since the Ferris Wheel began moving to t=10 seconds since the Ferris Wheel started moving.   What was the change in Sam's height above the ground as the amount of time since the Ferris Wheel started moving increases from 4 seconds to 10 seconds?   Use function notation to represent the average rate of change of Sam's height above the ground (in feet) in terms of the amount of time (in seconds) since the Ferris Wheel started moving on the interval from t=4 to t=10.   Determine the value of the average rate of change (represented in part e) of Sam's height above the ground (in feet) in terms of the amount of time (in seconds) since the Ferris Wheel started moving, as t increases from 4 to 10 seconds. Select an answer feet seconds feet per second seconds per foot

The number of books in a community college library increases according to the function B-7200,000 where t is measured in years. How many books will the library have after 8 year(s)? OA 7,200 OB. 9,153 OC 10275 OD. 4462 CHO

An investment appreciates 2% per year. Originally $5000 is invested. What is an equation to model this where F is the value of the investment and t is the years that passes. OF = 5000(0.98)t F = 500(1.02)t OF = 5000(-0.02)t OF = 5000(0.02)t

Under a microscope, Ms. Kapinski studies a culture with bacteria. As the number of hours progresses, Ms. Kapinski sees that the bacteria can be modeled by the function ?(?) = 1290(0.76) ? where b represents the number of bacteria t hours after Ms. Kapinski begins her study. (a) What does the value 0.76 represent in this situation? Be sure to explain. (b) What does the value 1290 represent in this situation? Be sure to explain. (c) The number of bacteria in a second study is modeled by the function ?2 (?) = 1180(1.76) ? . i. What does the value of 1180 represent in this situation? ii. What does the difference of 1290 and 1180 mean between the two studies? iii. What does the difference between 0.76 and 1.76 mean between the two studies?

A driver has to pay an annual road tax of $150. His car does 50 kilometers to one gallon which costs 50 cents per gallon. The car is serviced every 5000 kilometers at a cost of $40, and depreciation is calculated in cents by multiplying the square of the mileage by 0.01. (I) If he covers x kilometers in a year, compute an expression for the total cost in traveling x kilometers and the average total cost per kilometer. (ii) Show that the annual mileage which will minimize the average total cost per kilometer is around 1049 miles.

An item costs x dollars and then a 20% discount is applied. Select ALL the expressions that could represent the price of the item after the discount? A. (20/100)x B. x - (20/100)x C. (1-0.20)x D. (100-20/100)x E. 0.80x F. (100-20)x