i need help with question 3 and 4!!!

i need help with question 3 and 4!!!


MAT1193 Bio Calculus Test #2 Review – Things You Need to Know! • Be able to use shortcut rules to find derivatives (whether written out problems or applications) and be able to interpret results (if application); be able to find maximum/minimums of these functions. o Power Rule o Chain Rule o Product Rule o Quotient Rule o LN and ?? o Trigonometric functions • Understand the logistic growth function and understand how to find and interpret the following: o Carrying capacity o Inflection point (point of diminishing returns) o Solve for a particular value (see population example 1 in class) • Understand the surge function and understand how to find and interpret the following: o Maximum value (by graph and/or solving) o Minimum effective concentration o Growth rate o Value of 1 ? and meaning • Understand the difference between inflection and critical point in a real-world setting and be able to find both. Practice Problems – You Should Be Able to Work ANY like these Find all critical points and prove if a max or a min for the following ?(?) = ?4 − 4?3 on 1 ≤ ? ≤ 4 Give the actual (x,y) values (Logarithmic and Chain Rule) A research group using hospital records develop the following mathematical model relating systolic blood pressure and age: ?(?) = 40 + 25ln⁡(? + 1) for 0 ≤ ? ≤ 65. P(x) is pressure, measured in millimeters of mercury, and x is age in years. What is the rate of change of pressure at the end of 10 years? For this model what is the minimum and maximum systolic blood pressure? (Product Rule and exponential OR Surge Function) The drug concentration in the bloodstream t hours after injection is given approximately by ?(?) = 4.35??−?⁡⁡⁡⁡ Where 0 ≤ ? ≤ 5 and ?(?) in concentration in milligrams per milliliter. What is the rate of change of the concentration after 1 hour? What does this tell you about the concentration at hour 1? [must prove] (Logistic Function) The rabbit population, P, in a wilderness area is approximated by the function ? = 800 1 + 18?−0.24? where t is the number of weeks since the rabbits were introduced into the area. A. How many rabbits were initially introduced into the area (to the nearest rabbit)? B. How many rabbits were in the area after 5 weeks (to the nearest rabbit)? C. What is the carrying capacity of rabbits in the area? D. In how many weeks will the rabbit population reach 400? What is this value and its meaning? (Trigonometric Function and Quotient Rule) An algae population in an aquarium starts out growing at a slow rate and then takes off with accordance to the model ? = 3? sin⁡(?) where {0 ≤ ? ≤ ?} where x is in hours (in terms of ?) and y is the number of algae colonies. Predict the rate that the algae is growing at ? 2 . (Trig with Chain Rule) Normal human body temperature fluctuates with a rhythm tied to our sleep cycle. If ?(?) is body temperature in degrees Celsius at time ? in hours since 9am, modeled by ?(?) = 36.8 + 0.6 sin ( ? 12 ?) At 1pm, is the body temperature increasing or decreasing and give this in Celsius degrees per hour.