Question

Polio drops are delivered to 50 K children in a district. The rate at which polio drops are given is directly proportional to the number of children who have not been administered the drops. By the end of 2^nd week half the children have been given the polio drops. How many will have been given the drops by the end of 3^rd week can be estimated using the solution to the differential equation `"dy"/"dx" = "k"(50 - "y")` where x denotes the number of weeks and y the number of children who have been given the drops.

Which of the following solutions may be used to find the number of children who have been given the polio drops?

Options

• y = 50 - e^kx

• y = 50 - e^=kx

• y = 50(1 - e^-kx)

• y = 50 (e^=kx - 1)

Answer 1

y = 50(1 - e^-kx)