How can you tell from an exponential equation if it's a growth or decay model?

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How can you tell from an exponential equation if it's a growth or decay model?

A growth equation will have a base that is equal to or greater than 1.

f(x)=2* [tex]5^{x}[/tex] is a growth equation because 2 is greater than 1.

f(x)=.24*[tex]5^{x}[/tex] is a decay equation because .24 is less than 1.

Step-by-step explanation:

ok we know that exponential functions have exponent at the top the funtions.

the general form of exponential function is [tex]f(x)=y=a^x[/tex].

we know that x is the exponent here.

if we have positive value of x .

we can say that exponential function is increasing or growth function.

if we have negative value of x it is decreasing or decay.

exponential function for decay is [tex]f(x)=y=a^-x[/tex].

where x is decreasing in decay function.

But sometimes things can grow (or the opposite: decay) exponentially, at least for a while.

So we have a generally useful formula:

y(t) = a × ekt

Where y(t) = value at time "t"

a = value at the start

k = rate of growth (when >0) or decay (when <0)

t = time

Step-by-step explanation:

The general form of an exponential equation for growth is

[tex]y=(1+r)^x[/tex]

and for decay is

[tex]y=(1-r)^x[/tex]

In general, if the number inside the parenthesis (the growth or decay rate) is greater than 1, it's a growth problem. If the number inside the parenthesis is greater than 0 but less than 1 (in other words a positive fraction), it's a decay problem.