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The number of children in a church is increasing at a rate that is proportional to the number of children present each year. The church starts out with 4 children, and after 3 years there are 15 children. Find the number of children after 5 years. intent 12.01 Semester Test: Calculus Round to the nearest child. O 72 Calculus 36 18 A boat purchased for $25,000 depreciates exponentially. After one year, the car is valued at $20,000. 0 9 How fast is the value of the boat depreciating after two years? culus Decrease $8001 per year O Decrease $3730 per year Increase $3730 per year O Increase $8001 per year Assume an object's weight, W, is proportional to its height, H. Does it make sense to use differential equations to model the Weight of the object? 4 90 91 92 93 94 95 96 If so, write the differential equation. If not, explain why. Yes, all = HK is a differential equation with a rate of change. No, W = KH is a differential equation with a rate of change. No, W = KH is a simple relationship and there is no rate of change so no need to use differential equations. Yes, it = # is a differential equation with a rate of change. MacBook Air 2 3 6 8 Assume that a population of deer, P, is inversely proportional to the number of elk, E. W Does it make sense to use differential equations to model the population size? If so, write the differential equation. If not, explain why. Yes, " = is a differential equation with a rate of change. No, P = is a simple relationship and there is no rate of change so no need to use differential equations. O No, P = KE is a simple relationship and there is no rate of change so no need to use differential equations. 19 Yes, le = KE is a differential equation with a rate of change. Iculus Assume that a population P of wolves in a region changes inversely to the area A of the region. Does it make sense to use differential equations to model the population size? The interest on an account ncreases exponentially. if an initial investment of $5000 earns $900 in two years, what is the rate of increase at the end of that second year If so, write the differential equation. If not, explain why. $500.00 O No, P = KA is a simple relationship and there is no rate of change so no need to use differential equations. $488.52 Yes, = is a differential equation with a rate of change. $462.17 $450.00 Yes, = KA is a differential equation with a rate of change. 4 90 91 92 93 94 95 96 97 98 No, P = is a simple relationship and there is no rate of change so no need to use differential equations. 35bZe_daat20ac-ede0-412-980a-64560890ccad/ce A bank pays continuous compounded interest. Jim deposits $1,000 in the account and in 10 years he has $1,250. MacBook Air Write the differential equation for A(t), the amount of money in Jim's account at time t. A(1) = 1250e0.02231 12.01 Semester Test: Calculus o A(1) = 10e0.02231 Iculus O A(1) = 1000e0.0223: O A(1) = 1000e10r The amount of a radioactive substance, y, decays expo ightspace.co Viewer/2969417?url=https%34%2F21/59af8a9-95/5-419c-a486-ace0599ad923.sequence... ( #@ sample decays to exactly half in that time period. Write a differe dths.myschoolapp.. O n in terms of y and t, in days, to represent the rate of de 12.01 Semester Test: Calculus di =-0.0433y E 0 - = 0.1732y OR ulus O - = -0.08663 0 "= -0.1732y 1 90 91 92 93 94 05 96 97 98 90 Fin If a population of endangered salmon, S(t), starts out with 80 fish and decreases at a rate proportional to 0.02 times the number of fish present each year, write the particular solution to the differential equation which describes the number of fish over time. Let t be measured in years O S(1) = 80e0.021 MacBook Air o S(1) = 80e-0.021 o S(1) = 100e0.02 o S(1) = 100e-0.21 5 6 90 91 92 93 94 95 96 97 98 99 Next
