Robert buys six guppies.Every two months, the guppy population quadruples.

Question

Write an exponential function to model the situation ( use months ). 

What is the population after 1 month?

How many will it take the population to reach 500 guppies?

Answer 1

The question requires an exponential function as a answer. We know an exponential function has the following format: X^y = Z where X is our starting value, Y is our time factor, and Z is our total value.

 

We start with a population of 6. This starting population doesn't change. Every two months the population quadruples. However, the answer wants the equation where the variable is one month. Thus, our exponent (y value), our time factor, is 0.5y. Next is to see where the exponent goes. We know the exponent goes on the 4 (for quadruple) and not the 6, because the population is quadrupled each time a set amount of time (y value) passes. The starting population (6) does not change as time changes. Thus your equation is:

 

6 x 4^0.5y = Z

 

Where y is the amount of time in months, and Z is your final population.

 

After one month you will have: Z = 12 guppies

 

The population will take: 6.38 months

 

Further hints:

I. If you get confused about where to put the exponent, try plugging in a simple time (2 months) and see if your answer is logical.

II. Don't forget your units on your answers! Robert bought guppies, not numbers.