Continuous Compounding and Exponential Functions

Continuous Compounding and Exponential Functions

Assessment

Interactive Video

Mathematics

9th - 12th Grade

Practice Problem

Hard

Created by

Patricia Brown

FREE Resource

The video tutorial covers the concept of base e and natural logarithms, explaining their properties and significance in mathematics. It discusses exponential growth and decay, and how these functions relate to their inverses, the natural logarithms. The tutorial also demonstrates how to convert between exponential and logarithmic forms, solve equations and inequalities using natural logs, and apply these concepts to continuous compounding interest calculations.

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10 questions

Show all answers

1.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What is the approximate value of the natural base 'e'?

3.14159

2.71828

1.61803

1.41421

2.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

Which function represents exponential growth when the exponent is positive?

f(x) = x^e

f(x) = e^(-x)

f(x) = ln(x)

f(x) = e^x

3.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

How is the natural logarithm of a number 'x' commonly written?

e^x

log_e(x)

ln(x)

log(x)

4.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

Convert the exponential equation e^7 = x into logarithmic form.

ln(7) = x

log(x) = 7

ln(x) = 7

log_e(x) = 7

5.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What is the result of e raised to the power of ln(x)?

e^x

1

ln(x)

x

6.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

Solve for x: 3 * e^(-2x) = 6.

x = ln(1)/-2

x = ln(6)/-2

x = ln(2)/-2

x = ln(3)/-2

7.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What is the formula for continuous compounding interest?

A = P * e^(n * t)

A = P * (1 + rt)

A = P * e^(R * T)

A = P * (1 + r/n)^(nt)

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