Exponential Applications Part 2
.pdf
School
Sharpstown H S**We aren't endorsed by this school
Course
MATH 101
Subject
Mathematics
Date
Dec 16, 2024
Pages
2
Uploaded by ChefHippopotamus6820
Name: ________________________ 1.Complete the table below.2.Describe what happens to (1 +1π₯)π₯as π₯gets bigger and bigger. 3.Eulerβs number, π β 2.71828 β¦, is a mathematical constant. Notice above that as πapproachesinfinity, (1 +1π₯)π₯approachesπ.a)Substitute π=π₯πinto the compound interest formula: π΄=P(1+ππ)ππ‘. Simplify. b)Rewrite your expression from part a) as an expression in terms of π₯raised to the ππ‘power.c)Based on your previous answers, rewrite the compound interest formula considering whathappens as xapproaches infinity. This is called a continuous compound interest formula (wherethe number of compounding periods approaches infinity).x (π +ππ)πx (π +ππ)π10 10,000 100 100,000 1,000 1,000,000 Earlier, we learned about compound interest calculations. What happens to your interest rate calculations as the number of compounding periods approaches infinity? Knowledge Quest:
Key Takeaways: 1.Your schoolβs math teamwants to buy new calculators. They invest $1500 in a savings account with 5% interest. a)Calculate the amount of money they will after 2 years if interest compounds semi-annually? b)Calculate the amount of money they will after 2 years if interest compounds monthly? c)Calculate the amount of money they will after 2 years if interest compounds continuously? 2.You invest $2500 in a savings account with a fixed annual interest rate that compounds continuously. After 10 years, the account reaches a balance of $4788.85. What is the interest rate of the account? The Double G: Gauge (Your) Grasp: