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# Determine the type of graph Increasing Linear, Decreasing Linear, Positive Quadratic, Negative Quadratic, Exponential Growth, or Exponential decay and give proof.

Question
Exponential growth and decay
Determine the type of graph Increasing Linear, Decreasing Linear, Positive Quadratic, Negative Quadratic, Exponential Growth, or Exponential decay and give proof.

2020-11-21
The curve for a linear equation is always a straight line.
From the given graph, it can be seen that the given curve is not a straight line. Hence, the given graph is not increasing linear or decreasing linear.
The curve for a quadratic equation is always a parabola parallel to Y-axis.
From the given graph, it can be seen that the given curve is not a parabola. Hence, the given graph is not a graph of negative quadratic or positive quadratic function.
The curve for any exponential function passes through the point (0,1).
From the given graph, it can be seen that the given curve passes through the point (0,1). Hence, the given graph is either the graph of exponential growth or exponential decay function.
But it can be seen that the given graph is an increasing graph. Thus, the given graph is the graph for an exponential growth function.

### Relevant Questions

The number of teams y remaining in a single elimination tournament can be found using the exponential function $$\displaystyle{y}={128}{\left({\frac{{{1}}}{{{2}}}}\right)}^{{x}}$$ , where x is the number of rounds played in the tournament. a. Determine whether the function represents exponential growth or decay. Explain. b. What does 128 represent in the function? c. What percent of the teams are eliminated after each round? Explain how you know. d. Graph the function. What is a reasonable domain and range for the function? Explain.
Determine whether the function represents exponential growth or exponential decay. Then graph the function.
$$\displaystyle{y}={\left({0.8}\right)}^{{{x}}}$$
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(a) Identify what the equation
$$=y8000(1.09)^x$$ illustrates.
Quadratic growth, linear decay. linear growth, quadratic decay, expotential growth, or expotential decay
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$$y=450 \cdot 2^x$$
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$$\displaystyle{y}={3}{\left({1.88}\right)}^{{t}}$$