A model for the yield of an agricultural crop as a function of the nitrogen level N and phosphorus level P in the soil is Y (N, P) = kN P e-N-P where k is a positive constant. What levels of nitrogen and phosphorus results in the best yield

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A strain of bacteria is placed into a nutrient broth at 30° Time (hr), t Population (g), P C and allowed to grow. The data shown to the right are collected. The population is measured in grams and the time in hours. Since population P depends on time t and each input corresponds to exactly one output, we say that population is a function of time; so P(t) represents the population at time t. 0 NM 50 50 2.5 3.5 4.5 6 (a) Find the average rate of change of the population from 0 to 2.5 hours. On average, the population is increasing at a rate of (Round to 3 decimal places as needed.) 0.02 0.18 0.23 0.35 0.51 gram per hour from 0 to 2.5 hours.

Glucose Concentration When glucose is infused into a per- son's bloodstream at a constant rate of c grams per minute, the glucose is converted and removed from the bloodstream at a rate proportional to the amount present. The amount of glucose in grams in the bloodstream at time t (in minutes) is given by g(1) rat + ( 80 a where a is a positive constant. Assume go = 0.08, c = 0.1, and a = 1.3. (a) At what time is the amount of glucose a maximum? What is the maximum amount of glucose in the bloodstream? (b) When is the amount of glucose in the blood-stream 0.1 g? (c) What happens to the amount of glucose in the blood- stream after a very long time?

D3 Assume an hypothetical consumer faced by the following utility function; U=X^2Y ( squared times y). After a bad harvest and thus bad economic conditions, the price of good X increases from Ksh.4.2 to Ksh. 4.8, while the price of good Y which was ksh. 4 increased to ksh.5. The income of the consumer was ksh. 30 before and after the good harvest. Calculate the CV and EV.

Charging the Capacitor Having stabilized the fuel, you look to your computer for next steps. You are told that the spacecraft uses "start capacitor" that must reach a required voltage in order to start its engine. This voltage is determined by the fixed capacitance and charge as a function of time, q (t). These capacitors are charged and stored in your current location and must be brought to the spacecraft. Your computer provides you with the following definitions: Charge: The charge as a function of time is q(t) = f i(t) dt, where i(t) = 18t5 + 20t³ 201³ - 20 is the current as a function of time. You need to provide the computer with the function g(t) in order for it to appropriately charge the start capacitor. If an unknown constant is needed, it can be included using "+ C", being sure to use a capital letter as the lowercase is used for capacitance. q (t)