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

a. The half-life of Moskiller is approximately 1.4 years using the rule of 70. b. After 6 years, approximately 305,260 mosquitoes would remain assuming a steady rate of decrease.

Step-by-step explanation:

a. The rule of 70 states that the number of years it takes for a quantity to double or halve can be approximated by dividing 70 by the percentage rate of growth or decline. In this case, the mosquitoes decrease by 50% per year. So, to find the half-life of Moskiller, we divide 70 by 50, which equals 1.4 years.

b. Assuming the rate is steady, we can use the half-life to find the number of mosquitoes remaining after 6 years. Since the half-life is 1.4 years, after 6 years, the number of half-lives would be 6 divided by 1.4, which is approximately 4.29. Using the formula N = N0 * (1/2)^(t/h), where N0 is the initial number of mosquitoes, t is the number of years, and h is the half-life, we can calculate the number of mosquitoes remaining as N = 2,450,000 * (1/2)^(4.29) ≈ 305,260.

Answer 2

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((1)/(2))^{(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((1)/(2))^{(6)/(1.4)}\approx125,614`

so, the answer will be:

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