How do you solve exponential equations?

To solve exponential equations, you can use logarithms. For example, to solve $$b^x = a$$ , take the logarithm of both sides: $$x = \frac{\text{log}(a)}{\text{log}(b)}$$ .

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 express the decay of a substance over time?

The decay of a substance over time can be expressed as $$N(t) = N_0 \times e^{-kt}$$ , where $$N_0$$ is the initial amount, $$k$$ is the decay constant, and $$t$$ is time.

What is the formula for continuous exponential growth?

The formula for continuous exponential growth is $$N(t) = N_0 e^{rt}$$ , where $$N_0$$ is the initial amount, $$r$$ is the growth rate, and $$t$$ is time.

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

To find the value of an exponential function at a specific point, substitute the value of $$x$$ into the function $$f(x) = a \times b^x$$ .

What is the relationship between exponential functions and logarithms?

Exponential functions and logarithms are inverse functions. If $$y = b^x$$ , then $$x = \text{log}_b(y)$$ .

How can you determine the growth factor from a given percentage increase?

To determine the growth factor from a percentage increase, convert the percentage to a decimal and add 1. For example, a 15% increase gives a growth factor of $$1 + 0.15 = 1.15$$ .

What is the formula for the area of growth in an exponential model?

The area of growth in an exponential model can be represented as $$A = \frac{P}{r} (e^{rt} - 1)$$ , where $$P$$ is the initial population, $$r$$ is the growth rate, and $$t$$ is time.

Exponential Functions Flashcards

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1.

FLASHCARD QUESTION

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What is an exponential function?

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2.

FLASHCARD QUESTION

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What does it mean for a value to decrease exponentially?

Back

A value decreases exponentially when it reduces by a constant percentage over equal intervals of time. For example, if a truck loses 15% of its value every five years, its value decreases exponentially.

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