Question 1

Which of the following best describes the number $$e$$?

Accepted Answer

$$e is an $$irrational number approximately equal to $$2.71828.$$

Question 2

Evaluate $$e^2$$ using the approximation $$e \approx 2.718.$$

Accepted Answer

$$e^2$$ \approx 7.389$$

Question 3

Which of the following is the correct domain for the function $$f(x) = e^x$$?

Accepted Answer

$$(-\infty, \infty)$$

Question 4

What is the range of the function $$f(x) = e^x$$?

Accepted Answer

$$(0, \infty)$$

Question 5

If $$f(x) = e$$^{x-2}$$, what is the effect of the -2$ in the exponent on the graph of f(x) = e^x$?

Accepted Answer

It shifts the graph 2 units to the right.

Question 6

Which real-world scenario can be modeled by an exponential function with base $$e$$?

Accepted Answer

Continuous compound interest in a bank account.

Question 7

Given $$f(x) = e^x$$ and $$g(x) = 2^x$$, which statement is true about their graphs?

Accepted Answer

Both have the same $$y-$$intercept at $$(0,1).$$

Question 8

If $$f(x) = e$$^{-x}$$, what transformation has been applied to f(x) = e^x$?

Accepted Answer

Reflection over the $$y-$$axis.

Question 9

Evaluate $$e^{0.5}$$ using $$e \approx 2.718 ($$round to three decimal places).

Accepted Answer

$$e^{0.5}$$ \approx 1.649$$

Question 10

Which of the following is NOT a property of the exponential function $$f(x) = e^x$$?

Accepted Answer

Its range is $$(-\infty, \infty).$$

Question 11

Suppose a population of bacteria grows according to $$P(t) = P_0$ e$$^{kt}$$, where P_0$ is the initial population and k$$ \u003e 0$$. What does k$ represent?

Accepted Answer

The continuous growth rate.

Question 12

If $$f(x) = e$$^{x+3}$$, how is the graph of f(x) = e^x$ transformed?

Accepted Answer

Shifted 3 units to the left.

Question 13

Which of the following best describes the end behavior of $$f(x) = e^x as$$ $$x 	o -\infty$$?

Accepted Answer

$$f(x) 	o 0$$

Question 14

A radioactive substance decays according to $$A(t) = A_0$ e$$^{-kt}$$. What does the negative sign in the exponent indicate?

Accepted Answer

The quantity is decreasing over time.

Question 15

Which of the following is the correct $$y-$$intercept for the function $$f(x) = e^x$$?

Accepted Answer

$$(0,1)$$

Question 16

If $$f(x) = e^x$$ and $$g(x) = e$$^{x-4}$$, how is the graph of g(x$$)$$ related to f(x$$)$$?

Accepted Answer

It is shifted 4 units to the right.

Exponential Functions and the Number e

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