Exponential Growth and Decay Flashcard (y=a(1+r)^t or y=a(1-r)^t)

Front

What is the general formula for exponential growth?

Back

y = a(1 + r)^t, where 'a' is the initial amount, 'r' is the growth rate, and 't' is time.

Front

What is the general formula for exponential decay?

Back

y = a(1 - r)^t, where 'a' is the initial amount, 'r' is the decay rate, and 't' is time.

Front

In the equation y = 500(1 + 0.08)^t, what does the '0.08' represent?

Back

The growth rate of 8%.

Front

What does the term 'initial amount' refer to in exponential models?

Back

The value of 'a' in the equations, representing the starting quantity before growth or decay.

Front

If a population is increasing by 5% per year, what is the value of 'r'?

Back

r = 0.05.

Front

How do you calculate the future value of an investment using exponential growth?

Back

Use the formula y = a(1 + r)^t, substituting 'a' for the initial investment, 'r' for the interest rate, and 't' for the number of years.

Front

What is the future value of an investment of $1000 at 6% interest compounded annually for 20 years?

Back

$1000(1.06)^20 = $3205.10.

Front

What is the population of rabbits in 2027 if there were 200 rabbits in 2020 and the population grows by 5% per year?

Back

281 rabbits.

Front

Write the exponential growth equation for a population of 200 rabbits increasing by 5% per year.

Back

P(t) = 200 * (1.05)^t.

Front

What does 't' represent in the exponential growth and decay formulas?

Back

The time in years.