Free Printable Exponential Models Involving Natural Base E

1.

Does the function represent exponential growth or decay?

a)

exponential growth because r>0

b)

exponential growth because r<0

c)

exponential decay because r>0

d)

exponential decay because r<0

2.

Simplify the expression, leaving e in the answer.

$e^3\cdot e^5$

a)

$e^{15}$

b)

$e^8$

c)

$2e^8$

d)

$2e^{15}$

3.

Simplify the expression, leaving e in the answer.

$\frac{11e^{10}}{22e^2}$

a)

$2e^5$

b)

$2e^8$

c)

$\frac{1}{2}e^5$

d)

$\frac{1}{2}e^8$

4.

Simplify the expression, leaving e in the answer.

\frac{27e^7}{3e^4}

a)

$9e^3$

b)

$24e^3$

c)

$9e^{\frac{7}{4}}$

d)

$24e^{\frac{7}{4}}$

5.

Solve 5e^{3x - 2} + 15 = 35

a)

13

b)

29

c)

10

d)

0.87

6.

Solve for x:
5 e^6x+3= 0.1

a)

-1.152

b)

0.232

c)

-3.077

d)

-0.854

7.

Solve for x:
e^x=7

a)

x=ln7

b)

x=ln⁷

c)

x=7^ln

d)

No solution

8.

Approximate the solution to the equation $4+e^x=19$ . Round to four decimal places.

(a)

9.

Log with a base "e" (log_e) is the same thing as...

a)

"e"

b)

Natural Logarithm (LN)

c)

Common Logarithm (Log)

d)

Natural Log, base "e"
LN_e

10.

What is the next step when solving the equation $2e^x-3=1$ ?

a)

$\ln x=2$

b)

$\ln2=x$

c)

$x=2$

d)

$\ln x=e^2$

11.

Use a calculator and/or desmos.com and round the irrational number $e$ to ten decimal places.

(a)

12.

Log with a base "e" (log_e) is the same thing as...

a)

"e"

b)

Natural Logarithm (LN)

c)

Common Logarithm (Log)

d)

Natural Log, base "e"
LN_e

13.

Simplify the expression, leaving e in the answer. $\left(5e^{7x}\right)^4$

a)

$5e^{11x}$

b)

$5e^{28x}$

c)

$625^{28x}$

d)

$625^{11x}$

14.

Without graphing, tell if the function below is growth or decay.

$y=4e^{3x}-2$

a)

Growth

b)

Decay

15.

Without graphing, tell if the function below is growth or decay.

$y=e^{-5x}$

a)

Growth

b)

Decay

16.

Simplify the expression, leaving e in the answer.

$e^{-4}\cdot e^6$

a)

$e^2$

b)

$e^{-24}$

c)

$2e^2$

d)

$2e^{-24}$

17.

You deposit $5,000 in an account that earns 3% interest compounded continuously. Which equation could be used to determine how much money would be in the account after 8 years?

a)

$A=5000e^{3\cdot8}$

b)

$A=5000e\cdot3\cdot8$

c)

$A=5000e\cdot0.03\cdot8$

d)

$A=5000e^{.03\cdot8}$

18.

You deposit $5,000 in an account that earns 3% interest compounded continuously. How much money would be in the account after 8 years? Round your answer to the nearest hundredth.

(a)

19.

Without graphing, tell if the function below is growth or decay.

$y=0.25e^{4x}$

a)

Growth

b)

Decay

20.

The approximate value of e is (a) . Use two decimal places.

Exponential Models Involving Natural Base E

Total questions: 20

Worksheet time: 20mins

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