Exponential Growth & Decay Equations & Examples

The population of a rural community was 3050 in 2010 and the population had increased to 3500 in 2015. Assuming exponential growth find the following.
a. The growth rate to 4 decimal places and as a percentage.
b. Estimate the population in 2018 if the trend continues.

Diego consumes an energy drink that contains caffeine. After consuming the energy drink, the amount of caffeine in Diegos

If k > 0, the equation ${\displaystyle y=y0e^{k}t}$ is a model for exponential (growth/decay), whereas if k >0, the equation is a model for exponential (growth,/decay).

Consider the following case of exponential growth. Complete parts a through c below.
The population of a town with an initial population of 75,000 grows at a rate of 5.5​% per year.
a. Create an exponential function of the form
$Q=Q_0\times (1+r)t$​, ​(where r>0 for growth and r<0 for​ decay) to model the situation described

Determine whether the function represents exponential growth or exponential decay. Then identify the percent rate of change. $y=10(1.07{)}^t$

Explain the mathematical model for the exponential growth or decay.

Describe a difference between exponential growth and logistic growth.

State whether the equation represents exponential growth, exponential decay, or neither.
${\displaystyle f\left(x\right)=18x^2}$

Write an exponential growth or decay function to model each situation. initial value: 50, growth factor: 1.15

Suppose that  f  is an exponential function with a percentage growth rate of  2% , and with $f(0)=147$. Find a formula for  f .
a) $f(t)=0.02t+147$
b) $f(t)=1.02(1.47)t$
c) $f(t)=147(1.02)t$
d) $f(t)=147(2)t$
e) $f(t)=147(1.20)t$

Tell whether the function represents exponential growth or exponential decay. Explain.
${\displaystyle y=3{\left(0.85\right)}^x}$

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.

State whether the equation represents exponential growth, exponential decay, or neither. $f(x)=5\cdot {0.3}^x$

Determine whether the function represents exponential growth or exponential decay. Identify the percent rate of change. $f(t)=4(1.05{)}^t$

Find the associated exponential decay or growth model.
Q=1,000 when t=0, half-life=1

At the beginning of an environmental study, ad forest covered an area of $1500k{m}^2$.Since then, this area has decreased by 3.75% each year.Let t be the number of years since the start of the study.Let y be the area that the forest covers in $k{m}^2$.
Write an exponential function showing relationship between y and t.

Population of Texas Texas was the third fastest growing state in the United States in 2016. Texas grew from 25.1 million in 2010 to 26.47 million in 2016. Use an exponential growth model to predict the population of Texas in 2025.

Determine whether the function represents exponential growth or exponential decay. Identify the percent rate of change. $y=3(1.88)ty=3(1.88{)}^t$

Tell whether the function represents exponential growth or exponential decay. Explain your reasoning.
${\displaystyle y=\left(\frac{1}{2}\right)e^{3}x}$

A regional rail company wants to reduce its delays. Presently, 70 percent of the trains arrive on time. The company’s goal is to improve this to 95 percent. What form of improvement trajectory will most likely occur?
a. Exponential growth
b. Exponential decay
c. Diminishing return growth