Find the equation of the curve that passes through the point (1, D) and has a slope of g at any point (x, y). 02:: 219% 3 22 2 09: 19+ 3 22 Oyzg 2 O _ 2:2_2 39 9 E If the rate of change in the number of children that attend a camival was found to be proportional to the square of the number of rides, write the differential equation that describes the rate of change in the number of children at the camival at a given time, t. Donotsolve. o %=% o %=M 0 %=k\\/C o %=k The rate of change in the number of cows, W, in a population is proportional to 150 - W(t), where t is measured in years. Write the differential equation to solve for W(t). Do not solve. 0 2 (150 W)k o % = (150 t)k O % : wokW o g = (150 + W)k If the acceleration A(t) of an object is inversely proportional to the square of its speed 3(t); write the differential equation for the acceleration of the object. Do not solve. o A(t)= % O: o Atti== A population P, is increasing proportional to (400 - P), and P never gets larger than 400. At t = 0 the size of the population is 10, at t = 4, the size of the population is 15. What is the size of the population at t = 10? Round to the nearest whole number. O 378 O 282 O 22 O 1The rate of change of S is directly proportional to 80:}, where 8(0) = 10 and 8(4) = 40. Find k, the proportionality constant. 0 k = 3.689 C1 k = 2.303 O k='1.386 O k=U.34T 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. Round to the nearest child. 0 72 O 36 O 18 OS An object's height is changing at a rate inversely proportional to its height. Does it make sense to use differential equations to model the height, H, of the object? If so. write the differential equation. If not, explain why. 0 No, H = kt is a simple relationship and there is no rate of change so no need to use differential equations. 0 Yes, = i is a differential equation with a rate of change. d: H 0 Yes, % = kH is a differential equation with a rate of change. 0 No, H 2 % is a simple relationship and there is no rate of change so no need to use differential equations