Question

The population of a parish is growing with an annual percentage rate compounded continuously. The population reaches 1.1 times its previous size in 2 years. Find the annual percentage rate according to the exponential growth function.Write your answer in exact form, using ln (do not round).

Answer 1

The annual percentage rate for continuous compound growth when the population reaches 1.1 times its size in 2 years is found using the function P = Pe^rt. By isolating the rate (r) and taking the natural logarithm, the rate is determined to be r = ln(1.1)/2.

Step-by-step explanation:

The annual percentage rate of a continuously compounded growth can be found using the formula P = Pert, where P is the new population size, Pe is the initial population size, r is the rate, and t is time. In this case, we want to find the value of r when the population is 1.1 times its original size (P = 1.1Pe) after 2 years (t = 2).

Setting up the equation:

• 1.1Pe = Pe2r

Divide both sides by Pe:

• 1.1 = e2r

Take the natural logarithm of both sides:

• ln(1.1) = ln(e2r) = 2r

Divide by 2 to solve for r:

• r = ln(1.1)/2

Therefore, the annual percentage rate for the continuous compound growth is r = ln(1.1)/2.