Exponential Growth and Decay Word Problems & Functions - Algebra & Precalculus
The Organic Chemistry Tutor・8 minutes read
The text discusses exponential growth and depreciation using various examples such as rabbit population, car value, house appreciation, and bacteria growth rates. It demonstrates how these formulas can be applied to calculate future values based on initial conditions and growth rates.
Insights
- The exponential growth equation y = a * b^x is essential for predicting population growth, where a is the initial population, b is 1 plus the growth rate, and x represents the number of years.
- Understanding exponential decay is crucial for calculating depreciation or reduction in value over time, with the formula y = a * (1 - r)^x, where a is the initial value, r is the rate of decrease, and x signifies the number of years.
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Recent questions
How do populations grow exponentially?
By multiplying initial amount by growth rate over time.
How does depreciation affect car value?
Car value decreases by a fixed percentage annually.
What is the impact of appreciation on property value?
Property value increases by a fixed percentage annually.
How do bacteria populations grow in samples?
Bacteria counts increase exponentially over time.
What is the significance of exponential growth in biology?
Exponential growth models bacterial populations accurately.
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Summary
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Exponential Growth and Depreciation Analysis
- In 2005, there were 1000 rabbits on an island, growing at a rate of 8% annually.
- The equation for exponential growth is y = a * b^x, with a representing the initial population and b as 1 + growth rate.
- By 2020, after 15 years, the rabbit population will be approximately 3172.
- A car valued at $40,000 in 2015 depreciates by 7% annually.
- In 2024, the car will be worth around $20,816.44.
- John's house, appreciating by 4% yearly, was valued at $225,000 in 2015.
- In 2002, he paid $135,129.17 for the house.
- Bacteria in a sample double every 20 minutes.
- After 3 hours, there will be 512,000 counts of bacteria.
- Another sample triples every 15 minutes.
- In one hour, there will be 8100 counts of bacteria.
- To reach 500 million counts, it will take 3.51 hours.
