Final answer:
It will take 3 years for an initially 100-strong unicorn population to reach 800 individuals if the population doubles every year.
Step-by-step explanation:
We are asked to determine the number of years it will take for a population of unicorns that grows exponentially to reach a population size of 800, starting with 100 unicorns and doubling every year. To solve this, we can use the formula for exponential growth:
P(t) = P0 * 2t
Where P(t) is the future population size, P0 is the initial population size, and t is the number of years. Here, P0 = 100 and P(t) = 800. We need to solve for t:
800 = 100 * 2t
8 = 2t
Since 23 = 8, it is clear that t = 3 years.
Therefore, it will take 3 years for the unicorn population to grow from 100 to 800 if it doubles every year.
Question: Considering exponential growth and decay, ponder upon the following scenarios. Solve for the unknown number of years in each of the following. (Do not round intermediate calculations and round your answers to 2 decimal places, e.g., 32.16.)
A population of unicorns grows exponentially, starting with 100 individuals and doubling every year. Determine the number of years it takes for the unicorn population to reach 800.