# Very Simple exponential growth problem

• lmlgrey
In summary, the conversation discusses how to determine the value of an acre of farmland in 10 years, given an initial value of $500 per acre and a growth rate of \frac{0.4x^3}{sqrt(0.2x^4+8000)} dollars per year. The experts suggest using an integral to calculate the function D(t) (Dollar vs. Time) and adding the constant of integration to account for the initial value. The final answer may differ depending on whether a definite or indefinite integral is used. lmlgrey 1. It is estimated that x years from now the value of an acre of farmland will be increasing at the rate of $$\frac{0.4x^3}{sqrt(0.2x^4+8000)}$$ dollars per year. If the land is worth 500 per acre, how much will it be worth in 10 years? 2. Use integral Since the the function of money of time is the integral of the rate given, i integrated the function 0.4x ^3/sqrt(0.2x^4+8000)...The answer therefore represents D(t) (Dollar Vs. Time)... Then I substitue 10 years into the function, I got how much is it worth in 10 years. but the question is, what's the use of the detail "now its worth 500 per acre"? should i add 500 to the answer i have now? thanks! You have to include the constant of integration because you're working with an indefinite integral. For example, $\int x^2 dx$ = 1/3 x^3 + C Your function D(t) should be D(t) + C. D(0) + C should be equal to 500. Since "now" equals "0 years from now", another way to do exactly what Mark44 said is to use a definite integral from 0 to 10- and then, since the integral from "0 to 0" is 0, add the$500. I suspect that is what Imlgrey meant originally.

ok... It seems that i completely forgot the contant part :P
now I integrated the function and got:
D(x)= sqrt(0.2x^4+8000)+C
D(0)= sqrt(8000)+C
500= sqrt(8000)+C
C= 410.557
Then D(10) = sqrt(0.2*10^4+8000)+410.557= 510.557 acre ---- does it look right?

...also, if I do what Hallsofivy said, I would have
sqrt(0.2x^4+8000)+C|100

and solving that, I got a totally different answer...Did I do anything wrong?

## 1. What is exponential growth?

Exponential growth is a type of growth where the rate of increase is proportional to the current amount. This results in a rapid growth over time, as the larger the amount, the faster it grows.

## 2. How do you calculate exponential growth?

The formula for exponential growth is A = A0(1 + r)t, where A is the final amount, A0 is the initial amount, r is the growth rate, and t is the time period.

## 3. What is the difference between exponential growth and linear growth?

Exponential growth increases at an increasing rate, while linear growth increases at a constant rate. This means that exponential growth results in a much larger final amount compared to linear growth over the same time period.

## 4. What are some real-life examples of exponential growth?

Some examples of exponential growth include population growth, compound interest, and the spread of diseases. In all of these cases, the amount increases at an increasing rate over time.

## 5. How can exponential growth be limited or controlled?

Exponential growth can be limited or controlled by implementing measures such as population control, interest rate regulations, and disease prevention strategies. These measures aim to slow down the growth rate and prevent it from reaching unsustainable levels.

• Precalculus Mathematics Homework Help
Replies
5
Views
2K
• Precalculus Mathematics Homework Help
Replies
5
Views
2K
• Differential Equations
Replies
7
Views
2K
• Precalculus Mathematics Homework Help
Replies
11
Views
2K
• Precalculus Mathematics Homework Help
Replies
4
Views
1K
• General Math
Replies
3
Views
1K
• Precalculus Mathematics Homework Help
Replies
14
Views
7K
• Precalculus Mathematics Homework Help
Replies
1
Views
2K
• Calculus
Replies
7
Views
3K
• Precalculus Mathematics Homework Help
Replies
3
Views
2K