Exponential Functions Practice Questions
ATAR (Australia) · ATAR Mathematics Methods · 143 free MCQs with instant results and detailed explanations.
143
Total
24
Easy
84
Medium
35
Hard
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Sample Questions from Exponential Functions
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Q1
Easy
If the function f(x) = 2^x represents population growth, what does f(3) represent in this context?
A.
Population at time t = 3
B.
Population at time t = 2
C.
Population at time t = 1
D.
Population growth rate
Show Answer & Explanation
Correct Answer: A
In the context of population growth represented by f(x) = 2^x, f(3) indicates the population size at time t = 3.
Q2
Easy
Which of the following graphs represents an exponential function?
A.
A curve that rises steeply as x increases
B.
A straight line
C.
A parabola opening upwards
D.
A horizontal line
Show Answer & Explanation
Correct Answer: A
An exponential function features a graph that rises steeply as x increases, distinguishing it from linear or quadratic graphs.
Q3
Easy
Which of the following is the graph of the function f(x) = 2^x?
A.
A graph that increases rapidly as x increases.
B.
A straight horizontal line.
C.
A graph that decreases as x increases.
D.
A graph that oscillates between two values.
Show Answer & Explanation
Correct Answer: A
The function f(x) = 2^x is an exponential function where the base is greater than 1. As x increases, the value of f(x) increases rapidly, resulting in a graph that rises steeply. This is characteristic of exponential growth.
Q4
Medium
What is the value of 'k' in the exponential function f(x) = 3e^(2x) if f(0) = k?
A.
3
B.
6
C.
1
D.
0
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Correct Answer: A
At x = 0, f(0) = 3e^(2*0) = 3e^0 = 3*1 = 3. Therefore, k = 3.
Q5
Medium
If the function f(x) = 5 * 2^(3x) represents exponential growth, what is the doubling time of this function?
A.
1/3 log2(2)
B.
1/3
C.
1/5
D.
3
Show Answer & Explanation
Correct Answer: A
The doubling time can be calculated using the formula t = log2(2)/k, where k is the growth rate. Here, k = 3, thus t = 1/3 log2(2).
Q6
Medium
Which of the following statements about the function f(x) = 4e^(-x) is correct?
A.
It approaches 0 as x approaches infinity.
B.
It has a horizontal asymptote at y = 0.
C.
Both A and B are correct.
D.
It is unbounded as x approaches infinity.
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Correct Answer: C
As x approaches infinity, the exponential term e^(-x) approaches 0, confirming both statements A and B are correct.
Q7
Medium
If the graph of the exponential function f(x) = a * b^(cx) passes through the point (1, 8) and has a horizontal asymptote at y = 2, what is the value of 'a'?
A.
2
B.
8
C.
4
D.
1
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Correct Answer: A
Since the horizontal asymptote is at y = 2, this means a = 2. The function can be rewritten to confirm this value.
Q8
Hard
If the function f(x) = 3e^(2x) represents exponential growth, what is the derivative f'(x)?
A.
6e^(2x)
B.
3e^(2x)
C.
3e^(2)
D.
3e^(2x) + 2
Show Answer & Explanation
Correct Answer: A
The derivative f'(x) is found by applying the chain rule. The outer function is 3e^(u) where u = 2x, with a derivative of 3e^(u) * u' (where u' = 2). Thus, f'(x) = 3e^(2x) * 2 = 6e^(2x).
Q9
Hard
The population of a certain bacteria culture doubles every 3 hours. If the initial population is 500 bacteria, what will the population be after 12 hours?
A.
2000
B.
4000
C.
8000
D.
16000
Show Answer & Explanation
Correct Answer: C
The population doubles every 3 hours, so in 12 hours, which is 4 doubling periods, the population will be 500 * 2^4. Thus, 500 * 16 = 8000.
Q10
Hard
A population of bacteria doubles every 3 hours. If the initial population is 500, what will the population be after 12 hours?
A.
8000
B.
4000
C.
3000
D.
6000
Show Answer & Explanation
Correct Answer: A
The population doubles every 3 hours, so in 12 hours (which is 4 cycles of doubling), the population will be 500 * 2^4 = 500 * 16 = 8000.
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Exponential Functions — ATAR (Australia) ATAR Mathematics Methods Practice Questions Online
This page contains 143 practice MCQs for the chapter Exponential Functions in ATAR (Australia) ATAR Mathematics Methods. The questions are organized by difficulty — 24 easy, 84 medium, 35 hard — so you can choose the right level for your preparation.
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