Exponential growth and decay

Exponential growth and decay

Assessment

Flashcard

Mathematics

12th Grade

Hard

CCSS
HSF-IF.C.8B, HSF-LE.A.1A, HSF.LE.B.5

Standards-aligned

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15 questions

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1.

FLASHCARD QUESTION

Front

What is exponential growth?

Back

Exponential growth occurs when the growth rate of a value is proportional to its current value, leading to growth that accelerates over time. It can be modeled by the equation f(t) = a(1 + r)^t, where 'a' is the initial amount, 'r' is the growth rate, and 't' is time.

Tags

CCSS.HSF-LE.A.1A

2.

FLASHCARD QUESTION

Front

What is exponential decay?

Back

Exponential decay is the process of reducing an amount by a consistent percentage rate over a period of time. It can be modeled by the equation f(t) = a(1 - r)^t, where 'a' is the initial amount, 'r' is the decay rate, and 't' is time.

Tags

CCSS.HSF-IF.C.8B

3.

FLASHCARD QUESTION

Front

What does the variable 'a' represent in the exponential function f(t) = a(1 + r)^t?

Back

'a' represents the initial amount or starting value before any growth or decay occurs.

Tags

CCSS.HSF-IF.C.8B

4.

FLASHCARD QUESTION

Front

What does the variable 'r' represent in the exponential function?

Back

'r' represents the growth or decay rate expressed as a decimal.

Tags

CCSS.HSF-IF.C.8B

5.

FLASHCARD QUESTION

Front

How do you determine if a function models growth or decay?

Back

If the growth factor (1 + r) is greater than 1, the function models growth. If the decay factor (1 - r) is less than 1, the function models decay.

Tags

CCSS.HSF-IF.C.8B

6.

FLASHCARD QUESTION

Front

What is the formula for compound interest?

Back

The formula for compound interest is A = P(1 + r/n)^(nt), where A is the amount of money accumulated after n years, P is the principal amount (the initial amount of money), r is the annual interest rate (decimal), n is the number of times that interest is compounded per year, and t is the number of years.

7.

FLASHCARD QUESTION

Front

Calculate the total amount after 2 years for $2750 at 8% interest compounded annually.

Back

Using the formula A = P(1 + r/n)^(nt), we have A = 2750(1 + 0.08/1)^(1*2) = 2750(1.08)^2 = 2750 * 1.1664 = $3207.60.

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