To the nearest tenth, how many days will it be before the rumor spreads to half the carrying capacity? For the following exercises, use this scenario: The equation N(t) = 1200/1 + 199e−0.625t models..

For the following exercises, use this scenario: The equation N(t) = 1200/1 + 199e−0.625t models the number of people in a school who have heard a rumor after t days.

To the nearest tenth, how many days will it be before the rumor spreads to half the carrying capacity?

Expert Solution

Consider the population is written using the formula;

P(t) = 1200/(1 + 199e-0.625t)

The number of years its take for the population to reach half of its capacity is:

600 = 1200/(1 + 199e-0.625t)

600(1 + 199e-0.625t) = 1200

600 + 119400e-0.0625t = 1200

e-0.625t = (1200 – 600)/119400

e-0.625t = 0.005

Take natural log on both sides;

ln(e-0625t) = ln(0.005)

-0.625t = ln(0.005)

t = ln(0.005)/-0.625

= 8.5

Therefore, it takes 9 years its take for the population to reach half of its capacity.

Nabeel answered 1 year ago

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