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

eiraszero11cu
2021-12-15
Answered

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

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Exponential Growth and Decay

Exponential growth and decay problems follow the model given by the equation$A\left(t\right)=P{e}^{rt}$

-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$A\left(0\right)=P{e}^{0\times t}=P{e}^{0}=P$

-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

$A\left(t\right)=900{e}^{0.0534}$

where A(t) is the number of bacteria and t represents the time in minutes.

How long will t take for the number of bacteria to double? (your answer must be accurate to at least 3 decimal places.)

Exponential growth and decay problems follow the model given by the equation

-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

-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

where A(t) is the number of bacteria and t represents the time in minutes.

How long will t take for the number of bacteria to double? (your answer must be accurate to at least 3 decimal places.)

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From 2000 - 2010 a city had a 2.5% annual decrease in population. If the city had 2,950,000 people in 2000, determine the citys