Real Exponents and Exponential Functions

Problem: 1

Simplify:

Problem: 3

Simplify the expression.

Problem: 5

Simplify the expression.

Problem: 7

Simplify the expression.

Problem: 9

Simplify and Round your result to three decimal places.

Problem: 11

Simplify:

Problem: 13

Simplify:

Problem: 15

Solve the equation and also check if there is no solution for the equation:

Problem: 17

Solve the equation and also check if there is no solution for the equation:

Problem: 19

Solve the equation and also check if there is no solution for the equation:

Problem: 21

Solve the equation:

Problem: 23

Solve the equation:

Problem: 25

Solve for x

Problem: 27

Solve for x.

81^x 27^3–x

Problem: 29

If f(x) = 5^x,

(a) find f(3), f(1.5), f(0), f(–3)

(b) sketch the graph of y = f(x)

(c) Is the function f is exponential in nature?

Problem: 31

Find the y–intercept and the asymptote of the graph of the function:

y = 3^x

Problem: 33

Find the y–intercept and the asymptote of the graph of the function:

y = 5 · 4^{x –}¹

Problem: 35

Determine whether the function represents exponential growth or decay:

Problem: 37

Determine whether the function represents exponential growth or decay:

Problem: 39

Determine whether the function represents exponential growth or exponential decay:

Problem: 41

Determine whether the function represents exponential growth or exponential decay:

Problem: 43

Determine whether the function represents exponential growth or exponential decay:

Problem: 45

Graph the function. Does it model exponential growth or exponential decay?

f(x) = (3.2)^x

Problem: 47

Graph the function. Does it model exponential growth or exponential decay?

f(x) = 750(0.77)^x

Problem: 49

Graph y = 9 · 3^x

Problem: 51

Graph

Problem: 53

Graph and state the domain and range of the function:

y = 2 · 4^x^{– 1}

Problem: 55

Graph and state the domain and range of the function:

y = 3^x^{– 2} + 4

Problem: 57

Graph

And state the domain and range.

Problem: 59

Graph the equations in the same coordinate system:

y = 5^x and y = 5^x^{– 2}

Problem: 61

Compare the graphs of the following functions :

Problem: 63

Compare the graphs of the following functions :

Problem: 65

Compare the graphs of the following functions :

Problem: 67

How are the graphs ofy = 6^x and y = 6^–x related to each other?

Hint: Sketch the graphs of both functions between x values, –2 to 2.

Problem: 69

Find the value of b if the function y = b · 2^x passes through (3, 2).

Problem: 71

Does the function model exponential growth or exponential decay? Find the function's percent increase or decrease.

f(x) = 4(0.47)^x

Problem: 73

Does the function model exponential growth or exponential decay? Find the function's percent increase or decrease.

y = 5(2.3)^x

Problem: 75

Does the function model exponential growth or exponential decay? Find the function's percent increase or decrease.

Problem: 77

A survey taken in 2000 showed that the population of the Asian region is expected to be more than three times its population by 2050. Find the annual growth rate.

Problem: 79

Model the situation by writing an exponential function. Find the value of the function after four years.

A painting purchased for $15,000 appreciates by 3% per year.

Problem: 1

Simplify:

Problem: 3

Simplify the expression.

Problem: 5

Simplify the expression.

Problem: 7

Simplify the expression.

Problem: 9

Simplify and Round your result to three decimal places.

Problem: 11

Simplify:

Problem: 13

Simplify:

Problem: 15

Solve the equation and also check if there is no solution for the equation:

Problem: 17

Solve the equation and also check if there is no solution for the equation:

Problem: 19

Solve the equation and also check if there is no solution for the equation:

Problem: 21

Solve the equation:

Problem: 23

Solve the equation:

Problem: 25

Solve for x

Problem: 27

Solve for x.

81^x 27^3–x

Problem: 29

If f(x) = 5^x,

(a) find f(3), f(1.5), f(0), f(–3)

(b) sketch the graph of y = f(x)

(c) Is the function f is exponential in nature?

Problem: 31

Find the y–intercept and the asymptote of the graph of the function:

y = 3^x

Problem: 33

Find the y–intercept and the asymptote of the graph of the function:

y = 5 · 4^{x –}¹

Problem: 35

Determine whether the function represents exponential growth or decay:

Problem: 37

Determine whether the function represents exponential growth or decay:

Problem: 39

Determine whether the function represents exponential growth or exponential decay:

Problem: 41

Determine whether the function represents exponential growth or exponential decay:

Problem: 43

Determine whether the function represents exponential growth or exponential decay:

Problem: 45

Graph the function. Does it model exponential growth or exponential decay?

f(x) = (3.2)^x

Problem: 47

Graph the function. Does it model exponential growth or exponential decay?

f(x) = 750(0.77)^x

Problem: 49

Graph y = 9 · 3^x

Problem: 51

Graph

Problem: 53

Graph and state the domain and range of the function:

y = 2 · 4^x^{– 1}

Problem: 55

Graph and state the domain and range of the function:

y = 3^x^{– 2} + 4

Problem: 57

Graph

And state the domain and range.

Problem: 59

Graph the equations in the same coordinate system:

y = 5^x and y = 5^x^{– 2}

Problem: 61

Compare the graphs of the following functions :

Problem: 63

Compare the graphs of the following functions :

Problem: 65

Compare the graphs of the following functions :

Problem: 67

How are the graphs of y = 6^x and y = 6^–x related to each other?

Hint: Sketch the graphs of both functions between x values, –2 to 2.

Problem: 69

Find the value of b if the function y = b · 2^x passes through (3, 2).

Problem: 71

Does the function model exponential growth or exponential decay? Find the function's percent increase or decrease.

f(x) = 4(0.47)^x

Problem: 73

Does the function model exponential growth or exponential decay? Find the function's percent increase or decrease.

y = 5(2.3)^x

Problem: 75

Does the function model exponential growth or exponential decay? Find the function's percent increase or decrease.

Problem: 77

A survey taken in 2000 showed that the population of the Asian region is expected to be more than three times its population by 2050. Find the annual growth rate.

Problem: 79

Model the situation by writing an exponential function. Find the value of the function after four years.

A painting purchased for $15,000 appreciates by 3% per year.

Hotmath Practice Problems