Question

The population of a colony of mosquitoes obeys the law of uninhibited growth. Use this information to answer

(a) If N is the population of the colony and t is the time in days, express N as a function of t. Consider No is the original amount at t = 0 and k≠0 is a constant that represents the growth rate.
N(t) =
How long is it until there are 70,000 mosquitoes? About days. (Do not round until the final answer. Then round to the nearest tenth as needed

Answer 1

The population of a colony of mosquitoes can be expressed as a function of time using the law of uninhibited growth. To find how long it will take for the population to reach 70,000 mosquitoes, we can use the equation N(t) = No * e^(kt) and solve for t.

Step-by-step explanation:

The population of a colony of mosquitoes can be expressed as a function of time using the law of uninhibited growth.

The function N(t) = No * e^(kt) represents the population N at time t, where No is the original amount at t = 0 and k is a constant representing the growth rate.

To find how long it will take for the population to reach 70,000 mosquitoes, we can set up the equation:

70,000 = No * e^(kt)

Solving for t, we can rearrange the equation to:

t = ln(70,000/No) / k

Using the given information, we can substitute the values into the equation and solve for t.