Exponential Decay Formula Examples
Problem 1. Every day, a fully inflated child’s pool raft loses 6.6 percent of its air. 4500 cubic inches of air were originally stored in the raft. To indicate the loss of air, write an equation.
Solution:
The equation for exponential decay is y = a(1 – r)t.
Here, a = 4500, r = 6.6% or 0.066
Hence, y = 4500(1 – 0.066)t
⇒ y = 4500(0.934)t
Here y is the air in the raft in cubic inches after t days.
Problem 2. Find the amount of air in the raft after 7 days in the above problem.
Solution:
As per the above problem, y = 4500(0.934)t.
Here, t = 7. Then,
⇒ y = 4500(0.934)7
⇒ y ≈ 2790
Problem 3. A town’s population has been declining at a pace of around 0.3 percent per year on average. The population was 88647 in 2000. Create a formula to reflect the population since the year 2000.
Solution:
The equation for exponential decay is y = a(1 – r)t.
Here, a = 88647, r = 0.3% or 0.003
Hence, y = 88647(1 – 0.003)t
⇒ y = 88647(0.997)t
Problem 4. Find the population of the above town in 2010 if the trend continues.
Solution:
As per the above problem, y = 88647(0.997)t
Here, t = 2010 – 2000 = 10. Then,
⇒ y = 88647(0.997)10
⇒ y ≈ 86024 people
Problem 5. An investment of $4500 has been losing value at 2.5% annually. Write an equation to represent its value in t years.
Solution:
The equation for exponential decay is y = a(1 – r)t.
Here, a = 4500, r = 2.5% or 0.025
Hence, y = 4500(1 – 0.025)t
⇒ y = 4500(0.975)t
Problem 6. Find the value of the investment in 5 years for the above problem.
Solution:
As per the above problem, y = 4500(0.975)t.
Here, t = 5. Then,
y = 4500(0.975)5
⇒ y = $3964.93
or, y ≈ $3965
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Exponential Decay Formula
Exponential Decay Formula: A quantity is said to be in exponential decay if it decreases at a rate proportional to its current value. In exponential decay, a quantity drops slowly at first before rapidly decreasing. The exponential decay formula is used to calculate population decay (depreciation), and it can also be used to calculate half-life (the amount of time for the population to become half of its size).
In this article, we have provided the formula for Exponential Decay, along with some examples of it.
Table of Content
- What is Exponential Decay
- What is the Exponential Decay Formula?
- Exponential Decay Formula
- Properties of Exponential Decay
- Practice Problems on Exponential Decay Formula
- Conclusion of Exponential Decay