# Lesson Worksheet: Natural Exponential Functions Mathematics

In this worksheet, we will practice identifying, writing, evaluating, sketching, and analyzing natural exponential functions and their transformations.

**Q1: **

Let . Find .

**Q2: **

Let . Find . Round your answer to four decimal places.

**Q3: **

Find the intercepts and asymptotes of the graph of the function .

- A-intercept: 0, -intercept: , asymptote:
- B-intercept: , -intercept: 0, asymptote:
- C-intercept: , -intercept: 0, asymptote:
- D-intercept: 0, -intercept: 0, asymptote:
- E-intercept: 0, -intercept: , asymptote:

**Q4: **

Given that , find .

- A
- B
- C
- D
- E

**Q5: **

The diagram shows the graph of a function of the form for constants , , and .

Find the values of and and the sign of .

- A, , and is negative.
- B, , and is positive.
- C, , and is positive.
- D, , and is positive.
- E, , and is negative.

**Q6: **

The diagram shows the graph of a function of the form for constants , , and .

Find the values of and and the sign of .

- A, , and is negative.
- B, , and is positive.
- C, , and is negative.
- D, , and is positive.
- E, , and is negative.

**Q7: **

Which of the following is a possible graph of ?

- A
- B
- C
- D

**Q8: **

Which of the following is a possible graph of ?

- A
- B
- C
- D

**Q9: **

Differentiate with respect to .

- A
- B
- C
- D
- E

**Q10: **

Find the point on the curve where the tangent line has a slope of .

- A
- B
- C
- D
- E