The number of field mice in a certain pasture is given by the function 200 – 10t, where time t is measured in years. Express a differential equation that models the population of owls, P(t), that feed on the mice if the rate at which the owl population grows is proportional to the difference between the number of owls at time t and number of field mice at time t, for t > 0.

The half-life of krypton-91 (9Kr) is 10 s. At time t = 0 a heavy canister contains 4 g of this radioactive gas. (a) Find a function m(t) = m,2-t/h that models the amount of 91Kr remaining in the canister after t seconds. m(t) = 10 (b) Find a function m(t) = moe-rt that models the amount of 91Kr remaining in the canister after t seconds. (Round your r value to five decimal places.) m(t) = (c) How much 9'Kr remains after 1 min? (Round your answer to three decimal places.) (d) After how long will the amount of 9'Kr remaining be reduced to 1 µg (1 microgram, or 10-° g)? (Round your answer to the nearest whole number.) sec

Newton's Law of Cooling tells us that the rate of change of the temperature of an object is proportional to the temperature difference between the object and its surroundings. This can be modeled by the differential equation =k(TA), where T is the temperature of the object after t units of time have passed, A is dT dt the ambient temperature of the object's surroundings, and k is a constant of proportionality. Suppose that a cup of coffee begins at 179 degrees and, after sitting in room temperature of 62 degrees for 14 minutes, the coffee reaches 170 degrees. How long will it take before the coffee reaches 160 degrees? Include at least 2 decimal places in your answer. minutes

The half-life of krypton-91 (91Kr) is 10 s. At time t = 0 a heavy canister contains 4 g of this radioactive gas. (a) Find a function m(t) = mo2-t/h that models the amount of 91Kr remaining in the canister after t seconds. m(t) = (b) Find a function m(t) = moe-rt that models the amount of 91Kr remaining in the canister after t seconds. (Round your r value to five decimal places.) m(t) = (c) How much 91Kr remains after 1 min? (Round your answer to three decimal places.) 10 (d) After how long will the amount of 91Kr remaining be reduced to 1 ug (1 microgram, or 10-6 g)? (Round your answer to the nearest whole number.) wmnod sec R S D G V B alt in control option comimand Command