Basic Calculus

1) What is the correct representation of the statement "If y represents the amount of the quantity at a given time and t represents the time", where k is constant? A. dx = ky dy B. = ky ky D. MY = dy 2) This refers to the initial amount of the growing quantity in the equation where the amount of t is 0. A. y(0) B. y(1) C. y(2) D. y(3) 3) Given the differential equation dy _ 1 dt - y. What is the general solution of the separable differential 4 equation? all painso A. y = Ae4 B. y = - Ae4 C. y = the4 D. y = te 4 4) Given the differential equation dy x -. What is the general solution of the differential equation? dx y A. y = Vx- A B. y = Vx + A C. y = x2 - A D. y = x2 + A5) Suppose that a colony of ants grows exponentially. After 1 day, 100 lice are counted. After 3 days, 400 were counted. How many are there originally? A. 25 B. 50 C. 100 D. 200 6) 'Suppose that a colony of ants grows exponentially. After 1 day, 100 [ice are counted. After 3 days, 400 were counted. What is the exponential growth equation that you can create to solve the population of the colony? A. y = (25)2' B. y = (50)2' c. y": (100)2' D. y = (200)2' 7) Certain bacteria cells are being observed in an experiment The population doubles in 1 hour. if at the end of 3 hours, the population is 24,000." What is the exponential growth equation that you can create in order to solve the population of the bacteria? A. y = (6000)2r B. y = (12000)? C. y = (18000)? I). y = (24000)2' 8) The half-life of a radioactive substance refers to the amount of time it will take for the quantity to decay to haif as much as it was originally. Substance Q has a half~life of 20 years. If in 2015, 100g of Q was at hand, what is the exponential decay equation of the substance Q? I}; y I," f/ 25?)20 B 5 1 2 c 75 I)\" o 100 1 m A_ : v . : _ = , = y 2 y 2 y 2 y 2 For number 9-10. Given the problem "The rate of decay of radium is said to be proportional to the amount of radium present If the half-life of radium is 80 years and there are 300 grams on hand this year.\" 9) How much radium will be present in year 2177? A. 25 B. 50 C. 75 D. 100 10) What is the exponential decay equation of the radium? 1/ A 25 1 3/30 B 5 11% c 75(1T'I0 D 100 1 :40 -y- [a] .y ()[E -.V- 5 -)'- [g] l \\ I "