A pride of lions is growing at a rate of 0.5% per year, compounded continuously. If the growth rate continues, how many years will it take for the size of the pride to reach 275% of its current size?

Question

Round your answer up to the nearest whole number, and do not include units

Answer 1

The general formula for continuous exponential growth is A=A₀•e^rt, where A₀ is the initial amount, t is the elapsed time, and r is the rate of growth or decay. For this problem, r=0.005, so the formula is A=A₀•e^0.005t.

Since we want to know how long it takes of the amount to be 275% of the original amount, we can state that A=2.75A₀. Substituting that into our formula gives us 2.75A₀=A₀•e^0.005t. Dividing by A₀ yields 2.75=e^0.005t.

At this point we need to take the natural logarithm of both sides:

ln(2.75)=ln(e^0005t)

ln(2.75)=0.005t

t=ln(2.75)/0.005, which is approximately equal to 202.3

We round up to 203 years.