Assume that a population, P, is changing at a rate inversely proportional to 50 + P. Does it make sense to use differential equations to model the population size? If so, write the differential equation. If not, explain why. 0 Yes, % = k(50 l P) is a differential equation with a rate of change. 0 No, P = kt is a simple relationship and there is no rate of change so no need to use differential equations. 0 No, P = % is a simple relationship and there is no rate of change so no need to use differential equations. 0 Yes, % = is a differential equation with a rate of change. Assume that the distance, D, an object is thrown changes inversely proportional to the square root of the force exerted, F. Does it make sense to use differential equations to model the distance thrown? If so, write the differential equation. If not, explain why. 0 No, D = i is a simple relationship and there is no rate of change so no need to use differential equations. F 0 Yes, % = % is a differential equation with a rate of change. 0 Yes, % = % is a differential equation with a rate of change. 0 No, D = kF is a simple relationship and there is no rate of change so no need to use differential equations. A bank pays continuous compounded interest. Jim deposits $1 ,000 in the account and in 10 years he has $1,250. Write the differential equation for A0), the amount of money in Jim's account at time t. O A(t) = 108011223: 0 A(t) = 100030322?\" 0 A(t) = 100091\" 0 A\") = 1250803223: In 2005, 40 million homes included a two-car garage, G. In 2009, 42 million homes included a two-car garage. Assuming the rate of growth in the number of two-car garages, N1 is proportional to the number of two-car garages currently owned, in what year will there be 60 million homes that include a two-car garage? 0 2038 O 2028 O 2018 O 2015 A recreational vehicle purchased for $120,000 depreciates exponentially. After one year, the vehicle is valued at $81,000. How fast is the value of the vehicle depreciating after four years? O Decrease $4591 per year 0 Increase $3264 per year 0 Increase $2076 per year O Decrease $3264 per year The interest on an account increases 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? 0 $500.00 0 $488.52 0 $462.17 0 $450.00 The amount of a radioactive substance. y, decays exponentially such that its half-life is 8 days. In other words, the amount of any sample decays to exactly half in that time period. Write a differential equation in terms of y and t, in days, to represent the rate of decrease in the amount of the substance. [I 0 592017323; 0 \"'9 00433 E_' y 0 \"'9 01732 E__' 9 y 0 =0.0866y