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.
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.