Lesson 6.7.1
6.7.1 Exponential growth and decay Quiz: Pearson Edexcel Maths, Unit 6
20 questions
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Lesson 6.7.1, Exponential growth and decay: 20 multiple choice questions for the Pearson Edexcel Maths (9MA0), Unit 6: Exponentials and logarithms, written with Revision Ninja.
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The 20 questions
-
What letter usually represents the base of natural exponential growth and decay models?
- pi
- k
- x
- e
-
In the model P = P0 e^(kt), what does P0 represent?
- Initial value
- Growth rate
- Time period
- Final value
-
If k is positive in P = P0 e^(kt), does the model represent growth or decay?
- Decay
- Oscillation
- Constant
- Growth
-
If k is negative in P = P0 e^(kt), does the model represent growth or decay?
- Equilibrium
- Fluctuation
- Decay
- Growth
-
What calculus operation is used to find the rate of change in an exponential model?
- Integration
- Differentiation
- Factorisation
- Rationalisation
-
What is the derivative of e^(kt) with respect to t?
- e^(kt) / k
- e^(kt)
- kt e^(kt - 1)
- ke^(kt)
-
If dP/dt = kP, what type of differential equation models this situation?
- Quadratic
- Second order
- First order
- Linear algebraic
-
What initial algebraic technique solves the separable differential equation dP/dt = kP?
- Rationalisation
- Integration by parts
- Separate variables
- Factor theorem
-
If a population triples every 5 years, what is the exact growth factor per year?
- 3/5
- 5/3
- 3^(1/5)
- ln(3)/5
-
Find the exact decay constant k if a substance halves every 10 years.
- -ln(10)/2
- -ln(2)/10
- -0.5/10
- -10/ln(2)
-
What is the doubling time if the growth constant k is 0.05?
- 2 / 0.05
- 0.05 / ln(2)
- ln(2) / 0.05
- ln(0.05) / 2
-
If N = 50 e^(0.2t), what is the initial population when t = 0?
- 0.2
- 10
- e
- 50
-
What is lim (t to infinity) of P0 e^(-kt) for positive k and P0?
- 0
- 1
- Infinity
- P0
-
Which logarithm base is used to invert natural exponential equations?
- Base 2
- Base x
- Base e
- Base 10
-
Rewrite y = a e^(bt) by taking natural logs of both sides. What is ln(y)?
- ln(a) * bt
- ln(a) + bt
- b ln(a) + t
- a + bt
-
If plotting ln(y) against t yields a straight line, what is the vertical intercept?
- ln(a)
- a
- e^b
- b
-
If plotting ln(y) against t yields a straight line, what does the gradient represent?
- ln(b)
- b
- a
- ln(a)
-
A bacterial culture grows from 200 to 1600 in 3 hours. What is the growth multiplier?
- 1400
- 4
- 8
- 3
-
If radioactive decay follows M = 100 e^(-0.04t), what percentage remains at t = 0?
- 0%
- 96%
- 4%
- 100%
-
What mathematical restriction usually applies to the time variable t in real-world models?
- All real numbers
- t <= 0
- t >= 0
- t > 1
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