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6.02 Applications of exponential functions

Adaptive
Worksheet

Interactive practice questions

Consider the curve $y=4^x+3$y=4x+3.

a

Determine the $y$y-value of the $y$y-intercept of the exponential curve.

b

What is the domain of the function?

all real $x$x

A

$x\ge4$x4

B

$x>0$x>0

C

$x\ge3$x3

D
c

What is the range of the function?

Give your answer as an inequality.

d

Which of the following is the graph of $y=4^x+3$y=4x+3?

Loading Graph...

A

Loading Graph...

B

Loading Graph...

C
Medium
1min

The graph of $y=2^x$y=2x is displayed here.

Medium
2min

Consider the curve $y=2\left(3^x\right)$y=2(3x).

Medium
2min

The number of bees in a colony is initially measured and left to form a hive. The number of bees in the hive is measured each day over the course of one week. The function $H\left(x\right)=30\left(3\right)^x$H(x)=30(3)x is found to model the number of bees, $H$H, after $x$x days.

Hard
1min
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Outcomes

A2.F.2

The student will investigate and analyze characteristics of square root, cube root, rational, polynomial, exponential, logarithmic, and piecewise-defined functions algebraically and graphically.

A2.F.2a

Determine and identify the domain, range, zeros, and intercepts of a function presented algebraically or graphically, including graphs with discontinuities.

A2.F.2c

Determine the intervals on which the graph of a function is increasing, decreasing, or constant.

A2.F.2f

For any value, x, in the domain of f, determine f(x) using a graph or equation. Explain the meaning of x and f(x) in context, where applicable.

A2.F.2g

Describe the end behavior of a function.

A2.F.2h

Determine the equations of any vertical and horizontal asymptotes of a function using a graph or equation (rational, exponential, and logarithmic).

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