# Write an exponential function to model each situation. Find each amount after the specified time. A population of 120,000 grows 1.2% per year for 15 years.

Question
Exponential growth and decay
Write an exponential function to model each situation. Find each amount after the specified time. A population of 120,000 grows $$1.2\%$$ per year for 15 years.

2020-12-25
$$A(t) = a(1+r)^{t}$$
Substitude a with \$120,000, r with $$1,2\% = 0.012$$ and t with 15: $$A(15)=120,000(1+0.012)^{15}$$ $$=120,000(1.012)^{15}\approx 143,512$$ ### Relevant Questions asked 2021-01-06 Write an exponential growth or decay function to model each situation. Then find the value of the function after the given amount of time. The student enrollment in a local high school is 970 students and increases by 1.2% per year, 5 years. asked 2021-02-24 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 asked 2021-03-02 Write an exponential growth or decay function to model each situation. Then find the value of the function after the given amount of time. A new car is worth$25,000, and its value decreases by 15% each year, 6 years.
Write the exponential growth function to model the following situation:
A population of 422, 000 increases by 12% each year.
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
From 2000 - 2010 a city had a 2.5% annual decrease in population. If the city had 2,950,000 people in 2000, determine the city's population in 2008.
a) Exponential growth or decay:
b) Identify the initial amount:
c) Identify the growth/decay factor:
d) Write an exponential function to model the situation:
e) "Do" the problem.
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?