What does it mean for a function to be exponential?

A function is exponential if it can be expressed in the form $$f(x) = a \times b^x$$ , where $$a$$ is a constant and $$b$$ is a positive real number.

How do you find the value of an exponential function at a given point?

To find the value of an exponential function at a given point, substitute the value of $$x$$ into the function. For example, for $$A(t) = 20,000(0.88)^t$$ , substitute $$t$$ to find the value.

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.

How do you solve $$6^{3x} = 16$$ ?

Take the logarithm of both sides: $$3x \text{ln}(6) = \text{ln}(16)$$ , then solve for $$x$$ .

What is the formula for exponential decay?

The formula for exponential decay is $$A(t) = A_0 e^{-kt}$$ , where $$A_0$$ is the initial amount, $$k$$ is the decay constant, and $$t$$ is time.

How do you determine when an exponential function reaches a certain value?

Set the function equal to the desired value and solve for the variable. For example, to find when $$A(t) = 12,000$$ , set $$20,000(0.88)^t = 12,000$$ and solve for $$t$$ .

What is the relationship between exponential functions and logarithmic functions?

Exponential functions and logarithmic functions are inverses of each other. If $$y = b^x$$ , then $$x = \text{log}_b(y)$$ .

How do you solve $$6e^{\frac{x}{3}} = 1$$ ?

Divide both sides by 6, then take the natural logarithm: $$\frac{x}{3} = \text{ln}(\frac{1}{6})$$ , and solve for $$x$$ .

Resource Library

Math

Algebra

Exponential Equations

Solving Exponential Equations

Flashcard

•

Mathematics

•

10th Grade

•

Practice Problem

•

Easy

•

CCSS

HSF-IF.C.8B, HSF.LE.A.4, 5.NBT.A.4

Standards-aligned

Wayground Content

Used 1+ times

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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 with the same base?

Back

FLASHCARD QUESTION

Front

What is the natural logarithm?

Back

FLASHCARD QUESTION

Front

How do you use logarithms to solve exponential equations?

Back

FLASHCARD QUESTION

Front

What is the change of base formula for logarithms?

Back

FLASHCARD QUESTION

Front

How do you round a number to the nearest thousandth?

Back

To round a number to the nearest thousandth, look at the digit in the fourth decimal place. If it is 5 or greater, round up the third decimal place by one.

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