# 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 .
a) f(t)=0.02t+147
b) f(t)=1.02(1.47)t
c) f(t)=147(1.02)t
d) f(t)=147(2)t
e) f(t)=147(1.20)t The close connection between logarithm and exponential functions is used often by statisticians as they analyze patterns in data where the numbers range from very small to very large values. For example, the following table shows values that might occur as a bacteria population grows according to the exponential function P(t)=50(2t):
Time t (in hours)012345678 Population P(t)501002004008001,6003,2006,40012,800
a. Complete another row of the table with values log (population) and identify the familiar function pattern illustrated by values in that row.
b. Use your calculator to find log 2 and see how that value relates to the pattern you found in the log P(t) row of the data table.
c. Suppose that you had a different set of experimental data that you suspected was an example of exponential growth or decay, and you produced a similar “third row” with values equal to the logarithms of the population data.
How could you use the pattern in that “third row” to figure out the actual rule for the exponential growth or decay model? Consider the following case of exponential growth. Complete parts a through c below.
The population of a town with an initial population of 75,000 grows at a rate of 5.5​% per year.
a. Create an exponential function of the form
$$Q=Q0 xx (1+r)t$$​, ​(where r>0 for growth and r<0 for​ decay) to model the situation described In 1995 the population of a certain city was 34,000. Since then, the population has been growing at the rate of 4% per year.
a) Is this an example of linear or exponential growth?
b) Find a function f that computes the population x years after 1995?
c) Find the population in 2002 A "Student Drug Use and Health Survey" of Ontario high school students found that the percentage of students that reported serious psychosocial distress in the past month increased from 10.7% in 2013 to 17.1% in 2017.
Assuming a standard exponential growth trend, what is the annual growth rate in the percentage of students reporting serious psychosocial distress in the past month? The population (in millions) Ukraine in 2015 is 44.4 and the expected continuous annual rate of change k =−0.006.
(a) Find the exponential growth model P = Cekt for the population by letting t = 5 correspond to 2015.
(b) Use the model to predict the population of the country in 2030.
(c) Discuss the relationship between the sign of k and the change in population for the country. The population of a rural community was 3050 in 2010 and the population had increased to 3500 in 2015. Assuming exponential growth find the following.
a. The growth rate to 4 decimal places and as a percentage.
b. Estimate the population in 2018 if the trend continues.   