Question

A news item is spreading by word of mouth through a population of size 10,000 people. After t days, the number of people (in thousands) who have heard the news is given by the following equation.

y=f(t)=(10)/(1+150 e⁻⁰.¹ᵗ )

how many people have heard the news when its rate of spread is 1 thousand people per day?

Answer 1

To find the number of people who have heard the news when its rate of spread is 1 thousand people per day, we need to solve the equation y = f(t) = (10) / (1 + 150e^(-0.1t)) = 1.

Step-by-step explanation:

To find the number of people who have heard the news when its rate of spread is 1 thousand people per day, we need to solve the equation y = f(t) = (10) / (1 + 150e^(-0.1t)) = 1.

To solve this equation, we can start by multiplying both sides of the equation by (1 + 150e^(-0.1t)). This gives us 10 = 1 + 150e^(-0.1t).

Next, we can subtract 1 from both sides of the equation to isolate the exponential term. This gives us 9 = 150e^(-0.1t).

Lastly, we can divide both sides of the equation by 150 to solve for e^(-0.1t). This gives us 0.06 = e^(-0.1t).

To solve for t, we can take the natural logarithm of both sides of the equation. This gives us ln(0.06) = -0.1t.

Finally, we can divide both sides of the equation by -0.1 to solve for t. This gives us t = ln(0.06) / -0.1.

Using a calculator to evaluate this expression, we find that t ≈ 5.06 days.