If t is time in months, how long does it take for the hummingbird population to double?

Question

The size of a population of hummingbirds over time can be modeled by the equation p=55(2)^t/3. How can the constant 55 be interpreted? If t is time in months, how long does it take for the hummingbird population to double?

Answer 1

If you set t = 0, you get p = 55. This is the initial population of hummingbirds at the time the population is counted.

 

To determine the time for the population to double (reach 110), set p = 110 and solve for t.

 

Do you know how to do this? It ends up being the same as solving the equation

 

2 = 2^t/3 .

 

Let me know if you need help with this. (It's not really that difficult if you remember that 2 = 2¹.)