Free Printable Euler's Number

1.

If k is positive in e^kx, what happens as x increases?

a)

exponential growth

b)

decay

c)

grows in the negative direction

d)

stays constant

2.

If k is negative in e^kx, what happens as x increases?

a)

Growth

b)

Slow growth

c)

decays towards zero

d)

stays constant

e)

Gets large and negative

3.

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

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

a)

Growth

b)

Decay

4.

Use desmos.com or a graphing calculator to evaluate e^1.7 to 4 decimal places.

a)

5.4739

b)

4.6211

c)

2.7183

d)

4.8929

5.

Simplify: $e^{-2}\cdot e^6$

a)

$e^{-12}$

b)

$e^{-3}$

c)

$e^8$

d)

$e^4$

6.

$Simplify\ \ \ \frac{12e^{-7}}{8e^4}$

a)

$\frac{3e^3}{2}$

b)

$\frac{3}{2e^{11}}$

c)

$\frac{2e^3}{3}$

d)

$\frac{2}{3e^{11}}$

7.

$Simplify\ \ \left(4e^{-4x}\right)^7$

a)

$4e^{-28x}$

b)

$4^7e^{28x}$

c)

$\frac{4^7}{e^{28x}}$

d)

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

8.

If you invest $5,000 into an account paying 6% interest compounded continuously, how many years will it take until there is $8,000 in the account?

a)

7.83 years

b)

6.83 years

c)

9.67 years

d)

8.67 years

9.

You have a home worth $270,000 whose value is compounding continuously at a rate of 2% a year. Which of the following equations describe the value of the house after t years?

a)

$A\left(t\right)=27000e^{2t}$

b)

$A\left(t\right)=27000e^{0.02t}$

c)

$A\left(t\right)=27000\left(1.02\right)^t$

d)

$A\left(t\right)=27000\left(e+0.02\right)^t$

10.

Each year, a certain termite population continuously increases by 34.5%. Create an equation to model the number of termites in the population if there are initially 738 termites.

a)

$y=738e^{0.345t}$

b)

$y=738e^{1.0345t}$

c)

$y=\left(1+0.345\right)^t$

d)

$y=\left(e+0.345\right)^t$

11.

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)

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

Euler's Number

Total questions: 11

Worksheet time: 34mins

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