# Exponential Growth: Determine t When k=q

• intenzxboi
In summary, the conversation is discussing how to determine the period at which the function y = Cekt changes by a factor of q. The question is asking to find the value of T (period) when k=q. The conversation also touches upon the use of special characters in the expression and the importance of seeking help from tutors and other users in learning the material.
intenzxboi

## Homework Statement

Determine the period in which y = Cekt changes by a
factor of q.

I have no idea what it is asking.. find t when k=q?

The question is asking to find the T (period) such that

$$y\left(t+T\right) = q\cdot y\left(t\right)$$

y(t + T) = C ek^(t+T) = C e^kt+kT = C e^kt · e^kT = e^kT y(t).

so q= e^kT ??

intenzxboi said:
y(t + T) = C ek^(t+T) = C e^kt+kT = C e^kt · e^kT = e^kT y(t).

so q= e^kT ??
I'm afraid that my browser cannot render the special character that you have typed (the coefficient of T).

I'm sorry huh?

intenzxboi said:
I'm sorry huh?

A special character 'placeholder' appears before each T in your expression, I thought that you may have typed a special character?

Last edited:
intenzxboi said:
y(t + T) = C ek^(t+T) = C e^kt+kT = C e^kt · e^kT = e^kT y(t).

so q= e^kT ??
Yes, now solve for T.

HallsofIvy said:
Yes, now solve for T.
Thanks Halls. For some reason I was getting special characters inside intenzxboi's expressions.

Thanks guys.. without the help off all the tutors/mentor and other users i don't know how i will learn all this stuff

## 1. What is exponential growth?

Exponential growth is a type of population growth in which the growth rate is proportional to the current size of the population. This means that the population grows at an increasing rate over time.

## 2. What is the formula for determining t when k=q in exponential growth?

The formula for determining t when k=q in exponential growth is t = ln(q)/k, where t is the time, q is the final population size, and k is the growth rate.

## 3. How is exponential growth different from linear growth?

Exponential growth is different from linear growth in that the growth rate in exponential growth is constantly increasing, while in linear growth, the growth rate remains constant over time.

## 4. What are some real-life examples of exponential growth?

Some real-life examples of exponential growth include the spread of diseases, the growth of bacteria in a petri dish, and the increase in population size over time.

## 5. How is exponential growth used in scientific research?

Exponential growth is used in scientific research to model and predict population growth, as well as to study the spread of diseases and the growth of organisms in controlled environments. It is also used in fields such as economics and finance to study the growth of economies and investments.

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