Growth and decay calculus multiple choice questions, please help asap ill give helpful review

The rate of change of the population of bears is proportional to the initial population. Let P(t)be the number of bears in the population where fis measured in years. Use differential equations to nd the general solution for P(t), where 13(0) is the initial population and ris the rate of growth. 0 pa) = 8-\" o P(t) : P(0)e'\" 0 pa) = P(0)e'\" 0 pa) : er\" + 13(0) A radioactive isotope decays over time. A(t) is the amount of material. At t = 0 there is 15 kg and time t = 4 there is 5 kg. Write the particular solution to the differential equation which will describe the amount of isotope after time t. O A(t) = 15e(-0.333)t O A(t) = 5e(-0.333)t O A(t) = 15e(-0.275)t O A(t) = 15e(0.275)tNew-cars have a distinctive smell which is caused by the out-gassing of chemicals from the carpet, glues, and upholstery. Over time the chemicals in these items evaporate into the air at a rate proportional to N. You measured the "new car smell," N(t), as 100 when purchased and at i'= 6 months and there was N(t) : 1. Write and solve the differential equation which describes the amount of new car smell between t: D and t: 6 months, where tis measured in months. 0 N(t) : 100801767\" 0 N(t) = 100.9(4)-76m O N\") : '998(0.767)t O N(t) : 1004*0-99)' The rate of growth of wild horses is proportional to 2000 H, where H is the number of horses and is always less than 2000. Write the general differential equation to describe the number of horses, H(t), where t is in years. 0 H = 20005\" + 03 O H = 2000.94\" 0 H : 2000 + 033'\" O H = 2000 age-kt A bank pays compounded interest each year. Sue's account has $200 after 1 year with an interest rate of2%. Write the differential equation for the rate of change of the balance of the account, BU), overtime. 0 3m 2 196.049\"mt O B(t) : 20480'02t 0 3m 2 200.93% 0 B(t) : 20090112$