The number of yeast cells in a laboratory culture increases rapidly initially but levels off eventually. The population is modeled by the function a n = f(t) = 1 + be-0.6t where t is measured in hours. At time t = 0 the population is 20 cells and is increasing at a rate of 10 cells/hour. Find the values of a and b. a = 140 b = 60 According to this model, what happens to the yeast population in the long run? O The yeast population will grow without bound. O The yeast population will shrink to 0 cells. O The yeast population will stabilize at 5 cells. O The yeast population will stabilize at 60 cells. O The yeast population will stabilize at 120 cells.

The population of a town grows at a rate proportional to the population at time t. The initial population of 250 increases 20% in 9 years. What will the population be after 15 years? How fast is the population growing at t= 15?

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

The population, P, of kangaroos in a reservation is modelled by the logistic dP equation = dt 2P (5- reservation. - P 10 000 ) where t is measured in days. It is estimated that initially the population of the kangaroos is 15% of the carrying capacity of the (i) What is the initial population of the kangaroos? (ii) What is the population of the kangaroos when the rate of increase is a maximum?