Evaluate the function $$f(x)=3(2)^x$$ at $$x=-3$$ .

$$f(-3)=3(2)^{-3}=\frac{3}{8}$$ .

What does the equation $$S(t)=150(0.92)^t$$ represent?

This equation represents the number of sunflowers, S(t), in Sarah's garden over time, t, where the number of sunflowers decreases by 8% each month.

What is the rate of decrease in the equation $$S(t)=150(0.92)^t$$ ?

The rate of decrease is 8% each month, as indicated by the factor of 0.92.

What is the general form of an exponential decay function?

The general form of an exponential decay function is $$y = a(1 - r)^t$$ , where a is the initial amount, r is the rate of decay, and t is time.

What is the difference between rational and irrational numbers?

Rational numbers can be expressed as fractions of integers, while irrational numbers cannot be expressed as such and have non-repeating, non-terminating decimal expansions.

How do you identify a rational number from a set of numbers?

To identify a rational number, check if it can be expressed as a fraction of two integers. For example, $$\text{The square root of } 14$$ is not rational, while $$\text{The square root of } 64$$ is rational.

What is the formula for the volume of a cylinder?

The formula for the volume of a cylinder is $$V = \text{π}r^2h$$ , where r is the radius and h is the height.

What does it mean for a function to be exponential?

An exponential function is a mathematical function of the form $$f(x) = a \times b^x$$ , where a is a constant, b is a positive real number, and x is the exponent.

How do you evaluate an exponential function at a negative exponent?

To evaluate an exponential function at a negative exponent, use the property $$b^{-n} = \frac{1}{b^n}$$ . For example, $$f(-3) = 3(2)^{-3} = \frac{3}{8}$$ .

CTA Prep Upper/Honors 24-25 Flashcards

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15 questions

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1.

FLASHCARD QUESTION

Front

What is an irrational number?

Back

2.

FLASHCARD QUESTION

Front

What is a rational number?

Back

A rational number is any number that can be expressed as a fraction of two integers, where the denominator is not zero. Examples include integers, fractions, and terminating or repeating decimals.

3.

FLASHCARD QUESTION

Front

Identify an example of a rational number.

Back

4.

FLASHCARD QUESTION

Front

What is the significance of the square root of a perfect square?

Back

5.

FLASHCARD QUESTION

Front

What does it mean for a number to be 'not rational'?

Back

6.

FLASHCARD QUESTION

Front

How do you solve for the radius in a volume equation?

Back

7.

FLASHCARD QUESTION

Front

Back

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