Suggest a differential equation for which y vt is a solution
a quantity y y(t) is said to follow an exponential growth if it increases at a rate which is proportional to the amount present. assuming that the initial amount of the quantity present is yo we arrive at the following initial value problem. dy ky (k> 0) dt (1) y(0) = yo (a) solve the ivp using separation of variables (b) definition: the time it takes for the amount of the quantity to double its origi nal amount is called the doubling time, tp. show that the half-life for a quantity which follows the exponential decay model in 2 is tp (c) in a certain nutrient culture, a cell of the bacterium e. coli divides into 2 every 10 minutes. let y y(t) be the number of cells that are present t minutes after 6 cells are placed in the culture. assume that the growth of the bacteria obeys exponential growth. find a formula for y(t) and then use your model to determine how long (in minutes) it will take for the bacterial population to reach 600