Concept explainers
LIFE SCIENCE APPLICATIONS
Activity Level In the summer the activity level of certain type of lizard varies according to the time of day. A biologist has determine that activity level is given by the function
Where
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Calculus For The Life Sciences
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- Profit The yearly profit P for a widget producer is a function of the number n of widgets sold. The formula is P=180+100n4n2. Here P is measured in thousands of dollars, n is measured in thousands of widgets, and the formula is valid up to level of 20 thousand widgets sold. a. Make a graph of P versus n. b. Calculate P0 and explain in practical terms. What your answer means. c. What profit will the producer make if 15 thousand widgets are sold?. d. The break-even point is the sales level at which the profit is 0. Approximate the break-even point for this widget producer. e. What is the largest profit possible?arrow_forwardRunning Ants A scientist observed that the speed S at which certain ants ran was a function of T, the ambient temperature. He discovered the formula S=0.2T-2.7, Where S is measured in centimetres per second and T is in degrees Celsius. a. Using functional notation, express the speed of the ants when the ambient temperature is 30 degrees Celsius, and calculate that speed using the formula above. b. Solve for T in the formula above to obtain a formula expressing the ambient temperature T as a function of the speed S at which the ants run. c. If the ants are running at a speed of 3 centimeters per second, what is the ambient temperature?arrow_forwardDigital cameras A company that produces and sells digital cameras has determined that the total weekly cost C of producing x digital cameras is given by the function C(x)=1.5x2150x+4850. Determine the production level that minimizes the weekly cost for producing the digital cameras and find that weekly minimum cost.arrow_forward
- Cliff divers The height s, in feet, of a cliff diver is a function of the time t in seconds he has been falling. If s as a function of t can be expressed as st=-16t2+10t+300, what is the height of the diver at 3 seconds?arrow_forwardMaximum Revenue A small theater has a seating capacity of 2000.When the ticket price is 20,attendance is 1500.For each 1decrease in price, attendance increases by 100. (a) Write the revenue R of the theater as a function of ticket price x. (b) What ticket price will yield a maximum revenue? What is the maximum revenue?arrow_forward
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