Exponential Growth & Decay Equations & Examples

Indicate whether the function models exponential growth or exponential decay
${\displaystyle y=55e^{0.356t}}$
${\displaystyle y=69e^{-0.751t}}$
${\displaystyle y=55e^{-0.633t}}$
${\displaystyle y=222e^{-0.421t}}$

Define thew term Exponential Growth and Decay?

Given the function ${\displaystyle f\left(x\right)=630{\left(.64\right)}^x,}$ determine if this function models exponential growth or decay and identify the growth or decay rate.

The equation ${\displaystyle P\left(t\right)=504{\left(1.05\right)}^t}$ represents what kind of function? Which one is it?
Linear
Exponential decay
Exponential growth
Constant

Is that exponential growth or exponential decay?
${\displaystyle f\left(t\right)=70{\left(0.4\right)}^t}$

A colony of bacteria with an initial population of 8000 decays over time t (in hours) at a rate of 15% per hour.
a).Use the growth rate to write an exponential function to model the decay.
b). How long does it take for the population to be cut in half?

The equation ${\displaystyle y=250\times {1.04}^x}$ models
o exponential growth.
o exponential decay.
The rate of growth/decay is
O 4%.
O 96%.
O 104%.

Consider the model for exponential growth or decay given by ${\displaystyle A=A_0{e}^{kt}.}$
If k_____ , the function models the amount, or size,of a growing entity. If k_____ , the function models the amount, or size, of a decaying entity.

Exponential Growth and Decay ${\displaystyle A=A_0{e}^{kt}}$
Logistic Growth Model ${\displaystyle A=\frac{e}{1+a{e}^{-bt}}}$
Newton`s law of cooling ${\displaystyle T=C+(T_0-C)e^{kt}}$

A colony of bacteria with an initial population of 3000 grows over time t (in hours) at a rate of 22% per hour.
a). Use the growth rate to write an exponential function to model the growth.
b). How long does it take for the population to double?

Find the exponential function ${\displaystyle f\left(x\right)=C{a}^x}$ whose graph has the given points ${\displaystyle (0,2)}$ and ${\displaystyle (3,54)}$.

To begin a bacteria study, a petri dish had 2800 bacteria cells. Each hour since, the number of cells has increased by 2.3%

Identify the function as exponential growth or exponential decay.Then identify the growth or decay factor. $y=7\cdot {0.32}^x$

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

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

The count in a bacteria culture was 200 after 15 minutes and 1600 after 30 minutes. Assuming the count grows exponentially, what was the initial size of the culture? What was the doubling period?

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.

In how many different orders can five runners finish a race if no ties are allowed?

Exponential Growth and Decay Worksheet
1. ${\displaystyle y=55-{(1-0.02)}^{\prime }}$
a) Does this function represent exponential growth or exponential decay?
b) What is your initial value?
c) What is the rate of growth or rate of decay?
2. ${\displaystyle y=5575\times {\left(0.65\right)}^{\prime }}$
a) Does this function represent exponential growth or exponential decay?
b) What is your initial value?
c) What is the rate of growth or rate of decay?
3. ${\displaystyle y=14000\times {\left(0.92\right)}^{\prime }}$
a) Does this function represent exponential growth or exponential decay?
b) What is your initial value?
c) What is the rate of growth or rate of decay?

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