Exponential Growth & Decay Equations & Examples

Determine whether the function represents exponential growth or decay, Write the base in terms of the rate of growth or decay, identify R, and interpret the date of growth or decay. For the function ${\displaystyle y=150x{3.2}^x}$

Determine if it represents exponential growth or exponential decay.

State whether each statement is true or false and briefly explain why. If the statement is false, try to “fix it” by modifying the given statement to a new statement that is true. For exponential growth and decay, the rate of change is constant.

Exponential growth or exponential decay function ?

Given a geometric sequence 160, 80, 40, 20, ...
1) Find the 8th term of the sequence (in decimal form)
2) Find the sum of the first 8 terms of the sequence

A table for a function f is given to the right.
​(a) Determine whether function f represents exponential​ growth, exponential​ decay, or linear growth.
​(b) Find a formula for f.

Explain how zeros and end behavior of polynomial functions and their graphs are related to the degree and the factors of the polynomial.

Tell whether the function represents exponential growth or exponential decay. Then graph the function.
${\displaystyle f\left(x\right)=\frac{1}{3}{e}^x}$

Write an exponential growth or decay function to model each situation. Then graph each function. A boat that cost $45,000 is depreciating at a rate of 20% per year.

You learned about the row reduction matrix method for solving a system of linear equations. For example, consider the following system:

Graph each function and tell whether it represents exponential growth, exponential decay, or neither. y=-0.75

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

Determine whether the function represents exponential growth or exponential decay. ${\displaystyle y={\left(1.8\right)}^x}$

Tell whether the function represents exponential growth or exponential decay. ${\displaystyle f\left(x\right)=5{\left(2\right)}^{-x}}$

Compare exponential growth and exponential decay.

The function ${\displaystyle P=5{\left(1.07\right)}^t}$ represent exponential growth or decay. What is the initial quantity? What is the growth rate? State if the growth rate is continuous .

State whether the equation represents exponential growth, exponential decay, or neither. $y=0.82\cdot 3^x$

Identify the function as exponential growth or exponential decay.
${\displaystyle y=0.3\cdot {0.5}^x}$

Tell whether each function represents exponential growth, exponential decay, or neither. Justify your responses.

$\begin{array}{|ccccc|}\hline x& 0& 2& 4& 6\\ y& 1& 9& 81& 729\\ \hline\end{array}$

Tell whether the function represents exponential growth or exponential decay. Explain.
${\displaystyle y=2{\left(2.1\right)}^x}$