# Suppose that f is an exponential function with percentage growth rate of 5% and that f(0) = 5. Find a formula for f(x). f(x) =

Question
Exponential growth and decay
Suppose that f is an exponential function with percentage growth rate of 5% and that
f(0) = 5.
Find a formula for
f(x).
f(x) =

2020-11-24
Given that:
Suppose that f is an exponential function with the percentage growth rate of 5%
F(0)=5
By using,
The exponential equation is
$$F(x)=a(1+r)^x$$
Where a is the initial value and r is the growth rate/decay rate
By using above form of the exponential equation,
Here,
F(0)=5
Then we get
A=5
Growth rate=5%
=0.05
To get,
R=0.05
Plug the values of r=0.05 and a=5 in the above exponential form.
To get,
$$F(x)=5(1+0.05)^x$$
To get,
$$F(x)=5(1.05)^x$$
Therefore
$$F(x)=5(1.05)^x$$

### Relevant Questions

Suppose that  f  is an exponential function with a percentage growth rate of  2% , and with f(0)=147. Find a formula for  f .
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