Exponential Functions (Leaving Cert Mathematics): Quizzes

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Exponential Functions
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What is the general form of an exponential function?

f(x)=a×bxf(x) = a \times b^x

In f(x)=a×bxf(x) = a \times b^x, what does aa represent?

Initial value when x=0x = 0

For exponential growth, what must be true about the base bb?

b>1b > 1

For exponential decay, what range must bb fall within?

0<b<10 < b < 1

What is the domain of an exponential function?

All real numbers

If a>0a > 0, what is the range of f(x)=a×bxf(x) = a \times b^x?

f(x)>0f(x) > 0

Through which point does the graph of f(x)=a×bxf(x) = a \times b^x always pass?

(0,a)(0, a)

What is the horizontal asymptote of an exponential function?

y=0y = 0 (the xx-axis)

How does an exponential decay curve behave as xx increases?

Curves downwards

What is ∫ex dx\int e^x \, dx equal to?

ex+Ce^x + C

What is ∫a×bx dx\int a \times b^x \, dx equal to?

aln⁡(b)×bx+C\frac{a}{\ln(b)} \times b^x + C

If 100 bacteria double every 3 hours, how many are there after 6 hours?

400

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