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Algebra 1: Exponential Growth and Decay - Coggle Diagram
Algebra 1: Exponential Growth and Decay
Exponential Growth
Formula: y = a(1 + r)^t
Why is this important? Used for measuring...
Population Increases
"The population of the United States has been increasing at an average rate of 0.91%. If the population was about 303,146,000 in 2008, predict the population in 2020."
Growth of Monetary Investments
"Mr. Santiago received a job with an annual salary of $51,000. He will receive a 1.5% increase every year. How much will Mr. Santiago make in 3 years?"
Exponential Decay
Formula: y = a(1 - r)^t
Why is this important? Used for measuring...
Population Decreases
"In 2000, 2200 students attended ABC High School. The enrollment declines by 3% each year. How many students will be enrolled in 2020?"
Vehicle / Investment Depreciations
"Olivia buys a new car that costs $32,000. The value of the car is expected to depreciate 8% each year. Find the value of Olivia's car in 6 years."
Compound Interest
Formula: y = P(1+ r/n)^n*t
Why is this important? Used for determining...
The Final Amount of Invested Money
"Determine the amount of an investment if $500 is invested at an interest rate of 6.75% compounded quarterly for 10 years."
"Determine the value of an investment of $2500 if it is invested at an interest rate of 5.25% compounded monthly for 4 years."
Algebraic Terms
y - represents the final amount
a - represents the initial amount (Exponential Growth / Decay)
r - represents the rate of change (expressed as a decimal)
t - represents time
P - represents the initial amount (Compound Interest)
n - represents the number of times the interest is compounded each year
"monthly" - n = 12 "quarterly" - n = 4 "yearly" - n = 1