How do you find the time it takes for an investment to triple using continuous compounding?

To find the time it takes for an investment to triple, set $$A = 3P$$ in the formula $$A = Pe^{rt}$$ and solve for $$t$$ .

What is the value of $$e$$ ?

The value of $$e$$ is approximately 2.71828, and it is the base of the natural logarithm.

What is the process to solve $$10^x = 200$$ ?

1. Take the logarithm of both sides: $$\text{log}(10^x) = \text{log}(200)$$ . 2. Use the property of logarithms: $$x \text{log}(10) = \text{log}(200)$$ . 3. Solve for $$x$$ : $$x = \frac{\text{log}(200)}{\text{log}(10)} \text{ (approximately 2.30)}$$ .

How do you solve $$2e^{0.5x} = 44$$ ?

1. Divide both sides by 2: $$e^{0.5x} = 22$$ . 2. Take the natural logarithm: $$0.5x = \text{ln}(22)$$ . 3. Solve for $$x$$ : $$x = 2 \text{ln}(22) \text{ (approximately 6.18)}$$ .

What is the solution to $$-10 + 3e^x = 11$$ ?

1. Add 10 to both sides: $$3e^x = 21$$ . 2. Divide by 3: $$e^x = 7$$ . 3. Take the natural logarithm: $$x = \text{ln}(7) \text{ (approximately 1.95)}$$ .

How do you solve $$4^x - 6 = 10$$ ?

1. Add 6 to both sides: $$4^x = 16$$ . 2. Rewrite 16 as $$4^2$$ : $$4^x = 4^2$$ . 3. Set the exponents equal: $$x = 2$$ .

What does it mean to round to the nearest hundredth?

Rounding to the nearest hundredth means to round a number to two decimal places. For example, 2.345 rounded to the nearest hundredth is 2.35.

What is the significance of the base in an exponential function?

The base of an exponential function determines the rate of growth or decay. A base greater than 1 indicates growth, while a base between 0 and 1 indicates decay.

Resource Library

Math

Algebra

Exponential Equations

Solving Exponential Equations Using Logarithms

Flashcard

•

Mathematics

•

9th - 12th Grade

•

Practice Problem

•

Hard

•

CCSS

HSF.BF.B.5, HSF.LE.A.4, 5.NBT.A.4

Standards-aligned

Wayground Content

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15 questions

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FLASHCARD QUESTION

Front

What is an exponential equation?

Back

FLASHCARD QUESTION

Front

How do you solve an exponential equation using logarithms?

Back

FLASHCARD QUESTION

Front

What is the definition of a logarithm?

Back

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