5.3.1: Graphs and Properties of Exponential Growth and Decay Functions (Exercises)
SECTION 5.3 PROBLEM SET: GRAPHS AND PROPERTIES OF EXPONENTIAL GROWTH AND DECAY FUNCTIONS
In questions 1-4, let \(t\) = time in years and \(y\) = the value at time \(t\) or \(y\) = the size of the population at time \(t\). The domain is the set of non-negative values for \(t\); \(t ≥ 0\), because \(y\) represents a physical quantity and negative values for time may not make sense. For each question:
- Write the formula for the function in the form \(y = ab^t\)
- Sketch the graph of the function and mark the coordinates of the y-intercept.
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In questions 5-8, let \(t\) = time in years and \(y\) = the value at time \(t\) or \(y\) = the size of the population at time \(t\). The domain is the set of non-negative values for \(t\); \(t ≥ 0\), because \(y\) represents a physical quantity and negative values for time may not make sense. For each question:
- Write the formula for the function in the form \(y = ae^{kt}\)
- Sketch the graph of the function and mark the coordinates of the y-intercept.
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For questions 9-12
- Sketch a graph of exponential function.
- List the coordinates of the y intercept.
- State the equation of any asymptotes and state the whether the function approaches the asymptote as x →∞ or as x→ −∞ .
- State the domain and range.
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