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Exponential Functions Exploration
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Exponential Functions Exploration
Answer every question. Show your working for calculations, and include labels where you draw a graph.
Quick checks
1.For y = 6(1.4)^x, identify the values of a and b in the form y = ab^x.
- a = 6, b = 1.4
- a = 1.4, b = 6
- a = 6, b = 0.4
- a = 1, b = 6.4
2.For y = 3(2.5)^x, which statement correctly describes its domain, range and horizontal asymptote?
- Domain: all real x; range: y > 0; horizontal asymptote: y = 0
- Domain: x > 0; range: all real y; horizontal asymptote: x = 0
- Domain: all real x; range: y < 0; horizontal asymptote: y = 0
- Domain: y > 0; range: all real x; horizontal asymptote: y = 0
3.If f(x) = 7 × 3^x, what is f(0)?
- 0
- 1
- 3
- 7
4.Select every function below that represents exponential decay.
- p(x) = 8(0.75)^x
- q(x) = 4(1.08)^x
- r(x) = 6(1/3)^x
- s(x) = 2(1.2)^x
Evaluate, solve and apply
5.For f(x) = 3 × 2^x, calculate f(-2), f(2) and f(4).
6.Solve 5^x = 125.
7.Solve 2^(x + 2) = 32.
8.A laboratory sample contains 240 bacteria at the start of an observation. Its population triples every 4 hours. Write an exponential function B(t) for the number of bacteria after t hours.
9.Using B(t) = 240 × 3^(t/4), find the sample population after 8 hours.
10.Sketch B(t) = 240 × 3^(t/4) for 0 ≤ t ≤ 8. Label both axes and plot the values at t = 0, 4 and 8.
11.Ngaio invests $1,200 at 4% per year, compounded annually. Use A = P(1 + r)^t to find the balance after 5 years.
12.In the compound-interest model A = P(1.035)^t, explain what the base 1.035 means for the investment balance each year.
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