# 5.3.1: Graphs and Properties of Exponential Growth and Decay Functions (Exercises)

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## 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:

1. Write the formula for the function in the form $$y = ab^t$$
2. Sketch the graph of the function and mark the coordinates of the y-intercept.
 A house was purchased for $350,000 in the year 2010. The value has been increasing at the rate of 2% per year. A population of a certain species of bird in a state park has 300 birds. The population is decreasing at the rate of 7% year. A lab buys equipment$50,000. Its value depreciates over time. The value decreases at the rate of 6% annually. A population of bats in a cave has 200 bats. The population is increasing at the rate of 5% annually.

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:

1. Write the formula for the function in the form $$y = ae^{kt}$$
2. Sketch the graph of the function and mark the coordinates of the y-intercept.
 A population of 400 microbes increases at the continuous growth rate of 26% per day. The price of a machine needed by a production factory is $28,000. Due to inflation the price of the machine is increasing at the continuous rate of 3.5% per year. A population of an endangered species consists of 4000 animals of that species. The population is decreasing at the continuous rate of 12% per year. A business buys a computer system for$12000. The value of the system is depreciating and decreases at the continuous rate of 20% per year.

For questions 9-12

1. Sketch a graph of exponential function.
2. List the coordinates of the y intercept.
3. State the equation of any asymptotes and state the whether the function approaches the asymptote as x →∞ or as x→ −∞ .
4. State the domain and range.
 $$y=10\left(1.5^{x}\right)$$ $$y=10\left(e^{1.2 x}\right)$$ $$y=32\left(0.75^{x}\right)$$ $$y=200\left(e^{-0.5 x}\right)$$

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