How Do You Calculate the Limit of M*exp(D*exp(c*t)) as t Approaches Infinity?

[charlottewill]

Please could someone assist me with this question

Compute the limit of

lim t→∞ p(t)

where p(t) = M*exp(D*exp(c*t))

 

[Fantini]

Charlotte, could you please use LaTeX for your problem? Here's how:

\( p(t) = M \cdot \exp (D \cdot \exp (c \cdot t) ) \)

yields \( p(t) = M \cdot \exp (D \cdot \exp (c \cdot t) ) \). Also, what is D and what is c? Are they constants, if yes, do you have additional information about them? Can you post the problem in full?

 

[math771]

Sure, I'd be happy to help! To compute this limit, we can use the following steps:

1. First, let's rewrite the expression for p(t) as p(t) = M*e^(D*e^(c*t)). This will make it easier to work with.

2. Next, we can use the fact that e^(x) approaches infinity as x approaches infinity. This means that as t approaches infinity, the term e^(c*t) will approach infinity.

3. Since we have e^(c*t) in the exponent of p(t), we can rewrite p(t) as p(t) = M*e^(D*∞). This simplifies to p(t) = M*e^(∞), which is equal to infinity.

4. Therefore, the limit of p(t) as t approaches infinity is infinity, or in mathematical notation, lim t→∞ p(t) = ∞.

I hope this helps! Let me know if you have any further questions.