Question

In an effort to eradicate west Nile mosquitoes from Mosquito Town, you started spraying the town periodically with the chemical called Moskiller. It is estimated that the 2,450,000 mosquitoes decrease at the rate of 50% per year.a. Using the rule of 70, estimate the half-life of Moskiller. Round to two decimal places.b. Using the estimated half-life and assuming that the rate is steady, find the number of mosquitoes remaining after 6 years. Assume no new mosquitoes were born in that period.

Answer 1

Given:

The 2,450,000 mosquitoes decrease at the rate of 50% per year.

The general equation of the half-life time is:

$P(t)=P_0\cdot(\frac{1}{2})^{\frac{t}{h}}$

A) Using the rule of 70,

The half-life = 1.4 years

B) Using the estimated half-life and assuming that the rate is steady, find the number of mosquitoes remaining after 6 years.

so, we will substitute with:

t = 6 years and h = 1.4 years, to find the number after 6 years

So,

$P=2,450,000\cdot(\frac{1}{2})^{\frac{6}{1.4}}\approx125,614$

so, the answer will be:

The number of mosquitoes remaining after 6 years = 125,614