Question

Under certain circumstances a rumor spreads according to theequation: p(t) = 1/(1+ae⁻ᵏᵗ where p(t) is the proportion of thepopulation that knows the rumor at time t and a and k are positiveconstants.

a) Find limit as t approaches infinity.

Answer 1

The limit as t approaches infinity in the given equation is 0.

Step-by-step explanation:

The limit as t approaches infinity can be found by evaluating the expression lim p(t) as t approaches infinity. In this case, the expression p(t) = 1/(1+ae⁻ᵏᵗ). Let's break it down:

1. As t approaches infinity, the exponent ᵏᵗ approaches infinity as well.
2. e raised to the power of a very large number approaches infinity.
3. So the denominator of the fraction becomes very large, causing the fraction itself to approach 0.
4. Therefore, the limit as t approaches infinity is 0.