Create an example of sequence of numbers with an exponential growth pattern, and explain how you know that the growth is exponential.

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.

A fruit fly population of 24 flies is in a closed container. The number of flies grows exponentially, reaching 384 in 18 days. Find the doubling time (time for the population to double) and write an equation that models this scenario.

The population of a town increased by 2.54% per year from the beginning of 2000 to the beginning of 2010. The town's population at the beginning of 2000 was 74,860.

Exponential Growth and Decay
Exponential growth and decay problems follow the model given by the equation ${\displaystyle A\left(t\right)=P{e}^{rt}}$
-The model is a function of time t
-A(t) is the amount we have ater time t
-PIs the initial amount, because for t=0, notice how ${\displaystyle A\left(0\right)=P{e}^{0\times t}=P{e}^0=P}$
-Tis the growth or decay rate. It is positive for growth and negative for decay
Growth and decay problems can deal with money (interest compounded continuously), bacteria growth, radioactive decay. population growth etc.
So A(t) can represent any of these depending on the problem.
Practice
The growth of a certain bactenia population can be modeled by the function
${\displaystyle A\left(t\right)=900e^{0.0534}}$
where A(t) is the number of bacteria and t represents the time in minutes.
What is the number of bactenia ater 15 minutes? (round to the nearest whole number of bacteria.)

If f(x) is an exponential function where f(−1)=8 and f(8.5)=87, then find the value of f(3), to the nearest hundredth.

The function ${\displaystyle A=7.7{\left(0.92\right)}^t}$ represents an exponential growth or decay function.
A.
Does the function P represent exponential growth or decay? B. What is the initial quantity? C. What is the growth or decay factor?
a.
Exponential Growth. B. The initial quantity is 7.7. C. The growth or decay factor is 0.92
b.
Exponential Decay. B. The initial quantity is 7.7. C. The growth or decay facotor is 1.08
c.
Exponential Growth. B. The initial quantity is 0.92. C. The growth or decay factor is 1.08
d.
. Exponential Decay. B. The initial quantity is 7.7. C. The growth or decay factor is 0.92
e.
None of these

Define thew term Exponential Growth and Decay?