4.2-4.4 Solving Exponential Word Problems

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•
Mathematics
•
9th - 12th Grade
•
Hard
+2
Standards-aligned
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1.
FLASHCARD QUESTION
Front
What is the formula for continuous compound interest?
Back
A = Pe^(rt), 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), and t is the time the money is invested for in years.
2.
FLASHCARD QUESTION
Front
How do you calculate the interest rate when given the principal, amount after time, and time period for continuous compounding?
Back
Rearrange the formula A = Pe^(rt) to solve for r: r = (1/t) * ln(A/P).
3.
FLASHCARD QUESTION
Front
What does the variable 'a' represent in the exponential function y = ab^x?
Back
In the equation y = ab^x, 'a' represents the initial value or the y-intercept of the exponential function.
Tags
CCSS.HSF.LE.B.5
4.
FLASHCARD QUESTION
Front
How do you determine the total amount paid on a loan with compound interest?
Back
Use the formula A = P(1 + r/n)^(nt) for loans with compound interest, where A is the total amount, P is the principal, r is the annual interest rate, n is the number of times interest is compounded per year, and t is the number of years.
5.
FLASHCARD QUESTION
Front
What is the effect of increasing the compounding frequency on the total amount of interest earned?
Back
Increasing the compounding frequency results in more interest being earned, as interest is calculated and added to the principal more frequently.
6.
FLASHCARD QUESTION
Front
What is the growth rate of a population modeled by continuous exponential growth?
Back
The growth rate is expressed as a percentage and is used in the formula P(t) = P0 * e^(rt), where P0 is the initial population, r is the growth rate, and t is time.
7.
FLASHCARD QUESTION
Front
How do you calculate the future population of a growing bacteria culture using continuous growth?
Back
Use the formula P(t) = P0 * e^(rt), where P0 is the current population, r is the growth rate, and t is the time in the same units as the growth rate.
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