Mosquitoes and Formulas

Question

In a Minnesota swamp in the springtime (after the last frost) the number of mosquitoes per acre appears to grow according to the formula


N=10^0.1t+2
where t is the number of days since the last frost. What is the size of the mosquito population at times t=10 5=20 and t=30? What is the domain and range of this function?

NOTE: Remember this is a model of a "real world" phenomenon. Don't approach such tasks with "blind mathematics". Consider the real world implications before setting down the answer(s).

Show and Explain Your Work

Answer 1

Just plug in the values for t and find the exponent values.

For t=10, (0.1)(10)+2 = 1+2=3

N = 10³ = 1000

For t=20, (0.1)(20)+2 = 4

N = 10⁴ = 10,000

You can see the trend.

For t =30, N = 10⁵ = 100,000

 

Domain

The situation starts at the time of the last frost.  That's t=0.

We don't consider the time before that, so the domain is t≥0, or t = [0, ∞)

 

Range

At t=0, we have (0.1)(0)+2 =2

N = 10² = 100

There were 100 mosquitoes immediately after the last frost.

Range N≥100, or [100, ∞)

 

 

Note: If there were no constraints from the real world situation, domain would be -∞<t<∞, or t = (-∞, ∞).

Range would be 0<N<∞, or N = (0, ∞)