The equation =y8000(1.09)^x describes the amount of an investment (in dollars) based on the number of years it's been allowed to grow. (a) Identify what the equation =y8000(1.09)^x illustrates. Quadratic growth, linear decay. linear growth, quadratic decay, expotential growth, or expotential decay

The equation =y8000(1.09)^x describes the amount of an investment (in dollars) based on the number of years it's been allowed to grow. (a) Identify what the equation =y8000(1.09)^x illustrates. Quadratic growth, linear decay. linear growth, quadratic decay, expotential growth, or expotential decay

Question
Exponential growth and decay
asked 2020-12-05
The equation \(=y8000(1.09)^x\) describes the amount of an investment (in dollars) based on the number of years it's been allowed to grow.
(a) Identify what the equation
\(=y8000(1.09)^x\) illustrates.
Quadratic growth, linear decay. linear growth, quadratic decay, expotential growth, or expotential decay

Answers (1)

2020-12-06

We have the given equation is \(y=8000(1.9)^x\)
After seeing the equation it is clear that it is neither quadratic growth nor quadratic decay and it is also same for linear.
We also know that the exponential growth and decay is given by the formula
\(y=ab^x\) where ane0, the base bne1 and x is any real number.
Now, if \(b>1\)then the function represents exponential growth and if 0 Comparing the given function we get
\(a=8000\) and \(b=1.09>1\)
Therefore, we can say that the given equation is an exponential growth.

0

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