Log/Exp Test Review (2025)

Flashcard
•
Mathematics
•
11th - 12th Grade
•
Hard
Wayground Content
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15 questions
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1.
FLASHCARD QUESTION
Front
What is continuous compounding?
Back
Continuous compounding is the process of earning interest on an investment where the interest is calculated and added to the principal continuously, rather than at discrete intervals. The formula used is A = Pe^(rt), where A is the amount of money accumulated after time t, P is the principal amount, r is the annual interest rate, and t is the time in years.
2.
FLASHCARD QUESTION
Front
How do you calculate the average rate of return needed for continuous compounding?
Back
To calculate the average rate of return needed for continuous compounding, use the formula: r = (ln(A/P))/t, where A is the future value, P is the present value, and t is the time in years.
3.
FLASHCARD QUESTION
Front
What is the formula for continuous growth?
Back
The formula for continuous growth is N(t) = N0 * e^(rt), where N(t) is the amount at time t, N0 is the initial amount, r is the growth rate, and t is time.
4.
FLASHCARD QUESTION
Front
What does the variable 'r' represent in the context of continuous compounding?
Back
'r' represents the annual interest rate or growth rate expressed as a decimal in the context of continuous compounding.
5.
FLASHCARD QUESTION
Front
If you want to double your investment with continuous compounding, what is the approximate rate of return needed?
Back
To double your investment, you need an approximate rate of return of 69.3% per year, based on the rule of 70 (70/r = doubling time in years).
6.
FLASHCARD QUESTION
Front
What is the natural logarithm and how is it used in continuous compounding?
Back
The natural logarithm (ln) is the logarithm to the base e (approximately 2.718). It is used in continuous compounding to solve for time or rate in the formula A = Pe^(rt).
7.
FLASHCARD QUESTION
Front
How do you interpret a growth rate of 21% in a population model?
Back
A growth rate of 21% means that the population is increasing by 21% of its current size each year, leading to exponential growth over time.
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