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Worksheets11h 📗Q1
Total questions: 26
Worksheet time: 1hrs 21mins
What is the general form of an exponential function?
f(x) = a + b^x
f(x) = a * x^b
f(x) = a * b^x
f(x) = a - b^x
Sketch the graph of the function f(x) = 2^x. What are its key features?
The graph of f(x) = 2^x is a decreasing linear function.
The function has a maximum point at (0, 1) and decreases as x increases.
The graph passes through (1, 0) and approaches infinity as x approaches negative infinity.
The graph of f(x) = 2^x is an increasing exponential curve that passes through (0, 1), approaches 0 as x approaches negative infinity, and increases without bound as x approaches positive infinity.
Evaluate the exponential function f(x) = 3^x at x = 4.
27
81
64
100
Convert the exponential equation 5^x = 25 to logarithmic form.
log_5(1) = x
log_25(5) = x
log_5(25) = x
log_5(5) = x
Solve the equation 2^x = 16 for x.
2
4
10
8
If log_b(81) = 4, what is the value of b?
4
3
5
2
Solve for x: log_10(x) + log_10(5) = 2.
20
25
15
10
What is the value of x in the equation e^x = 7?
e^7
ln(1)
7^x
ln(7)
Convert the logarithmic equation log_2(32) = x to exponential form.
2^x = 64
2^x = 16
2^x = 8
2^x = 32
If f(x) = 4^x, what is f(3) and how do you calculate it?
16
256
64
32
In an exponential function, what does the 'a' represent?
Input
Rate of change
Y-intercept/Initial value
Output
In an exponential function, what does the 'b' represent?
Input
Rate of change
Y-intercept
Output
Suppose the population of a species of insects doubles every year. There are 1600 insects initially. The function for the scenario would be?
f(x)=2x+1600
f(x)=1600×2
f(x)=1600⋅2x
Is the following function an example of decay or growth?
f(x) = 2(1.25)x
Exponential Growth
Exponential Decay
log2(x + 2) + log2x = 3
Hint: condense first.
Rewrite the equation in logarithmic form.
R: all real numbers
R: y ≥ 0
R: y ≥ 3
R: y ≤ 3
Which equation is the inverse of the equation above?
