# Describe the shape of a scatter plot that suggests modeling the data with an exponential function. Question
Modeling Describe the shape of a scatter plot that suggests modeling the data with an exponential function. 2021-02-26
Step 1 The scatter plot that suggests modelling the data with an exponential function Have following properties. The data points on the graph should not be scattered far away from each other. The shape of the curve should either exponentially increasing upwards or exponentially decreasing downwards. Mostly the data points should be above the x - axis. Step 2 The one in which there is a declining trend in the data the graph of such datasets are called Exponentially decaying. While the other in which there is increasing trend is called exponentially increasing.

### Relevant Questions Describe the shape of a scatter plot that suggests modeling the data with an exponential function. Consider that algebraic modeling For the function $$\displaystyle f{{\left({x}\right)}}={34}{\left({1.024}\right)}^{x}$$
1) The function is an increasing exponential function because it is the form $$\displaystyle{y}={a}{b}^{x}$$ and ?
2) The growth rate is ?
3) Thrawth factor is ? Lemons and Car Crashes Listed below are annual data for various years. The data are weights (metric tons) of lemons imported from Mexico and U.S. car crash fatality rates per 100,000 population [based on data from “The Trouble with QSAR (or How I Learned to Stop Worrying and Embrace Fallacy),” by Stephen Johnson, Journal of Chemical Information and Modeling, Vol. 48, No. 1]. Is there sufficient evidence to conclude that there is a linear correlation between weights of lemon imports from Mexico and U.S. car fatality rates? Do the results suggest that imported lemons cause car fatalities? $$\begin{array}{|c|c|}Lemon imports &230&265&368&480&630\\ Crash FatalityRate&159&157&15.3&15.4&14.9\end{array}$$ An object moves in simple harmonic motion with period 5 seconds and amplitude 7 cm. At time $$\displaystyle{t}={0}$$ seconds, its displacement d from rest is -7 cm, and initially it moves in a positive direction.
Give the equation modeling the displacement d as a function of time t. An object moves in simple harmonic motion with period 8 minutes and amplitude 16 m. At time $$t = 0$$ minutes, its displacement d from rest is 0 m, and initially it moves in a positive direction. Give the equation modeling the displacement d as a function of time f. Determine the algebraic modeling which of the following data sets are linear and which are exponential. For the linear sets, determine the slope. For the exponential sets, determine the growth factor or the decay factor
a) $$\begin{array}{|c|c|}\hline x & -2 & -1 & 0 & 1 & 2 & 3 & 4 \\ \hline y & \frac{1}{9} & \frac{1}{3} & 1 & 3 & 9 & 27 & 81 \\ \hline \end{array}$$ b) $$\begin{array}{|c|c|}\hline x & -2 & -1 & 0 & 1 & 2 & 3 & 4 \\ \hline y & 2 & 2.6 & 3.2 & 3.8 & 4.4 & 5.0 & 5.6 \\ \hline \end{array}$$
c) $$\begin{array}{|c|c|}\hline x & -2 & -1 & 0 & 1 & 2 & 3 & 4 \\ \hline y & 3.00 & 5.0 & 7 & 9 & 11 & 13 & 15 \\ \hline \end{array}$$
d) $$\begin{array}{|c|c|}\hline x & -2 & -1 & 0 & 1 & 2 & 3 & 4 \\ \hline y & 5.25 & 2.1 & 0.84 & 0.336 & 0.1344 & 0.5376 & 0.021504 \\ \hline \end{array}$$ A common assumption in modeling drug assimilation is that the blood volume in a person is a single compartment that behaves like a stirred tank. Suppose the blood volume is a four-liter tank that initially has a zero concentration of a particular drug. At time $$\displaystyle{t}={0}$$, an intravenous line is inserted into a vein (into the tank) that carries a drug solution with a concentration of 500 mg/L. The inflow rate is 0.06 L/min. Assume the drug is quickly mixed thoroughly in the blood and that the volume of blood remains constant. a. Write an initial value problem that models the mass of the drug in the blood, for $$\displaystyle{t}\ \geq\ {0}$$. Solve the initial value problem, and graph both the mass of the drug and the concentration of the drug. c. What is the steady-state mass of the drug in the blood? d. After how many minutes does the drug mass reach 90% of its steady-state level? The annual sales S (in millions of dollars) for the Perrigo Company from 2004 through 2010 are shown in the table. $$\displaystyle{b}{e}{g}\in{\left\lbrace{a}{r}{r}{a}{y}\right\rbrace}{\left\lbrace{\left|{c}\right|}{c}{\mid}\right\rbrace}{h}{l}\in{e}\text{Year}&{2004}&{2005}&{2006}&{2007}&{2008}&{2009}&{2010}\backslash{h}{l}\in{e}\text{Sales, S}&{898.2}&{1024.1}&{1366.8}&{1447.4}&{1822.1}&{2006.9}&{2268.9}\backslash{h}{l}\in{e}{e}{n}{d}{\left\lbrace{a}{r}{r}{a}{y}\right\rbrace}$$ a) Use a graphing utility to create a scatter plot of the data. Let t represent the year, with $$\displaystyle{t}={4}$$ corresponding to 2004. b) Use the regression feature of the graphing utility to find an exponential model for the data. Use the Inverse Property $$\displaystyle{b}={e}^{{{\ln{\ }}{b}}}$$ to rewrite the model as an exponential model in base e. c) Use the regression feature of the graphing utility to find a logarithmic model for the data. d) Use the exponential model in base e and the logarithmic model to predict sales in 2011. It is projected that sales in 2011 will be \$2740 million. Do the predictions from the two models agree with this projection? Explain. An equation that expresses a relationship between two or more variables, such as $$\displaystyle{H}=\frac{9}{{10}}{\left({220}-{a}\right)}$$,
is called $$\displaystyle\frac{a}{{{a}{n}}} ?.$$ The process of finding such equations to describe real-world phenomena is called mathematical ? . ? An equation that expresses a relationship between two or more variables, such as $$H = \frac{9}{10} (20 - a)$$ is called a/an ? The process of finding such equations to describe real-world phenomena is called mathematical ? Such equations, together with the meaning assigned to the variables, are called mathematical ?