Question

1. In the following formula, where t is in hours, explain how to determine both doubling time and growth rate: x = 8 x 2^2t.

Answer 1

If the equation is as follows in the mathematical format as

x = 8 * 2^2t

Then the doubling time can be found out by taking log on both the side of the given equation that will give

log(x) = log 8 + 2t log 2

log(x) - log 8 = 2t log 2

log(x/8)/0.3010 = 2t

therefore, t= log(x/8)/0.6020

While for finding the growth rate then the differentiation of the equation which has been given has to take place.

dx/dt = 8 * 2^ (2t-1) * 2

dx/dt = 16 * 2^(2t-1)