# How can you tell whether an exponential model describes exponential growth or exponential decay?

Question
Exponential growth and decay
How can you tell whether an exponential model describes exponential growth or exponential decay?

2021-03-03
An exponential model is of the form $$A=A_0e^(kt)$$ where $$A_0$$ is the original amount or size of the entity at t = 0, A is amount or size at time t, and k is a constant representing the rate of growth decay.
If k > 0, then the model represents a growing quantity and k is called as the growth rate.
If k
So, we can tell whether an exponential model describes exponential growth or decay using the value of k.
Step 2
Conclusion:
Therefore, we can tell whether an exponential model describes exponential growth or decay using the value of k.

### Relevant Questions

Write an exponential growth or decay function to model each situation. Then find the value of the function after the given amount of time. A new car is worth \$25,000, and its value decreases by 15% each year; 6 years.
Determine whether each function represents exponential growth or exponential decay. Identify the percent rate of change.
$$\displaystyle{g{{\left({t}\right)}}}={2}{\left({\frac{{{5}}}{{{4}}}}\right)}^{{t}}$$

Tell whether the function represents exponential growth or exponential decay. Then graph the function. $$f(x)=(1.5)^{x}$$

Determine whether each equation represents exponential growth or exponential decay. Find the rate of increase or decrease for each model. Graph each equation. $$y=5^x$$

The close connection between logarithm and exponential functions is used often by statisticians as they analyze patterns in data where the numbers range from very small to very large values. For example, the following table shows values that might occur as a bacteria population grows according to the exponential function P(t)=50(2t):
Time t (in hours)012345678 Population P(t)501002004008001,6003,2006,40012,800
a. Complete another row of the table with values log (population) and identify the familiar function pattern illustrated by values in that row.
b. Use your calculator to find log 2 and see how that value relates to the pattern you found in the log P(t) row of the data table.
c. Suppose that you had a different set of experimental data that you suspected was an example of exponential growth or decay, and you produced a similar “third row” with values equal to the logarithms of the population data.
How could you use the pattern in that “third row” to figure out the actual rule for the exponential growth or decay model?

Determine whether the function represents exponential growth or exponential decay. Identify the percent rate of change. Then graph the function. $$y=5^x$$

The number of teams y remaining in a single elimination tournament can be found using the exponential function $$\displaystyle{y}={128}{\left({\frac{{{1}}}{{{2}}}}\right)}^{{x}}$$ , where x is the number of rounds played in the tournament. a. Determine whether the function represents exponential growth or decay. Explain. b. What does 128 represent in the function? c. What percent of the teams are eliminated after each round? Explain how you know. d. Graph the function. What is a reasonable domain and range for the function? Explain.
$$\displaystyle{y}={3}{\left({0.85}\right)}^{{x}}$$