Step-by-step solutions to hundreds of exponential model equations.

Which set of ordered pairs could be generated by an exponential function?
A. (1, 1) (2, 1/2) (3, 1/3) (4, 1/4)
B. (1, 1) (2, 1/4) (3, 1/9) (4 1/16)
C. (1, 1/2) (2, 1/4) (3, 1/8) (4, 1/16)
D. (1, 1/2) (2, 1/4) (3, 1/6) (4, 1/8)

zakinutuzi 2021-12-31 Answered

Furthermore why is it that $\displaystyle{e}^{{x}}$ is used in exponential modelling? Why aren't other exponential functions used, i.e. $\displaystyle{2}^{{x}}$, etc?

David Lewis 2021-12-30 Answered

I have a real valued number $\displaystyle{y}_{{t}}$. At each time step t, $\displaystyle{y}_{{t}}$ is multiplied by $\displaystyle{\left({1}+\epsilon\right)}$ with probability p and multiplied by $\displaystyle{\left({1}-\epsilon\right)}$ with probability $\displaystyle{1}-{p}$. What is the expected value of $\displaystyle{y}_{{{t}+{n}}}$? What is the variance?

Ikunupe6v 2021-12-21 Answered

What is the difference between linear growth and exponential growth?

Patricia Crane 2021-12-15 Answered

Find the derivative of $\displaystyle{y}={e}^{{{5}{x}}}$

Inyalan0 2021-12-09 Answered

Solve $\displaystyle{e}^{{{x}}}={0}$

Julia White 2021-12-09 Answered

Differentiate, please: $\displaystyle{y}={x}^{{{x}}}$.

lwfrgin 2021-09-21 Answered

Determine whether the given function is linear, exponential, or neither. For those that are linear functions, find a linear function that models the data. for those that are exponential, find an exponential function that models the data.
$\displaystyle{x}{F}{\left({x}\right)}-{1}{\left(\frac{1}{{2}}\right)}{0}{\left(\frac{1}{{4}}\right)}{1}{\left(\frac{1}{{8}}\right)}{2}{\left(\frac{1}{{16}}\right)}{3}\frac{1}{{32}}$

Lennie Carroll 2021-09-20 Answered

A researcher is trying to determine the doubling time fora population of the bacterium Giardia lamblia. He starts a culture in a nutrient solution and estimates the bacteria count every four hours. His data are shown in the table.
Time (hours)Bacteria count (CFU/mL)0374478631278161052013024173
Time (hours) 0 4 8 12 16 20 24
Bacteria count (CFU/mL) 37 47 63 78 105 130 173
Use a graphing calculator to find an exponential curve $f(t)=a*b^t$ that models the bacteria population t hours later.

Suman Cole 2021-09-20 Answered

Determine whether the given function is linear, exponential, or neither. For those that are linear functions, find a linear function that models the data. for those that are exponential, find an exponential function that models the data. xg(x) -12 05 18 211 314

avissidep 2021-09-18 Answered

James rents an apartment with an initial monthly rent of $1,600. He was told that the rent goes up 1.75% each year. Write an exponential function that models this situation to calculate the rent after 15 years. Round the monthly rent to the nearest dollar.

he298c 2021-09-16 Answered

A researcher is trying to determine the doubling time of a population of the bacterium Giardia lamblia. He starts a culture in a nutrient solution and estimates the bacteria count every four hours. His data are shown in the table. Use a graphing calculator to find an exponential curve f(t)=a⋅bt that models the bacteria population t hours later.
Time (hours) 04812162024 Bacteria count (CFU/mL)37476378105130173

DofotheroU 2021-09-13 Answered

The exponential growth models describe the population of the indicated country, A, in millions, t years after 2006.
Canada
$\displaystyle{A}={33.1}{e}^{{0.009}}{t}$ Uganda $\displaystyle{A}={28.2}{e}^{{0.034}}{t}$
Use this information to determine whether each statement is true or false. If the statement is false, make the necessary change(s) to produce a true statement. Uganda's growth rate is approximately 3.8 times that of Canada's.

Joni Kenny 2021-09-11 Answered

Determine whether the given function is linear, exponential, or neither. For those that are linear functions, find a linear function that models the data. for those that are exponential, find an exponential function that models the data. $$\begin{array} \text{x} & \text{g(x)}\ \hline \text{−1−1} & \text{3}\ \text{0} & \text{6}\ \text{1} & \text{12}\ \text{2} & \text{18}\ \text{3} & \text{30}\ \end{array}$$

Mylo O'Moore 2021-08-16 Answered

The following question consider the Gompertz equation, a modification for logistic growth, which is often used for modeling cancer growth, specifically the number of tumor cells. When does population increase the fastest in the threshold logistic equation $\displaystyle{P}'{\left({t}\right)}={r}{P}{\left({1}-{\frac{{{P}}}{{{K}}}}\right)}{\left({1}-{\frac{{{T}}}{{{P}}}}\right)}?$

Khadija Wells 2021-08-13 Answered

The table shows the annual service revenues R1 in billions of dollars for the cellular telephone industry for the years 2000 through 2006.

$\begin{matrix} Year&2000&2001&2002&2003&2004&2005&2006\\ R_1&52.5&65.3&76.5&87.6&102.1&113.5&125.5 \end{matrix}$
(a) Use the regression capabilities of a graphing utility to find an exponential model for the data. Let t represent the year, with t=10 corresponding to 2000. Use the graphing utility to plot the data and graph the model in the same viewing window.
(b) A financial consultant believes that a model for service revenues for the years 2010 through 2015 is $\displaystyle{R}{2}={6}+{13}+{13},{9}^{{0.14}}{t}$. What is the difference in total service revenues between the two models for the years 2010 through 2015?

Phoebe 2021-08-11 Answered

Find The Exponential Function $\displaystyle{f{{\left({x}\right)}}}={a}^{{x}}$ Whose Graph Is Given.

nicekikah 2021-08-08 Answered

For the following exercises, use a graphing utility to create a scatter diagram of the data given in the table. Observe the shape of the scatter diagram to determine whether the data is best described by an exponential, logarithmic, or logistic model. Then use the appropriate regression feature to find an equation that models the data. When necessary, round values to five decimal places.
$\begin{array}{|c|c|c|c|c|c|c|c|c|c|c|} \hline x & 3 & 4 & 5 & 6 & 7 & 8 & 9 & 10 & 11 & 12 & 13 \\ \hline \hline f(x) & 13.98 & 17.84 & 20.01 & 22.7 & 24.1 & 26.15 & 27.37 & 28.38 & 29.97 & 31.07 & 31.43 \\ \hline \end{array}$

illusiia 2021-08-06 Answered

Graph each function and tell whether it represents exponential growth, exponential decay, or neither. $\displaystyle{y}={\left({2.5}\right)}^{{{x}}}$

Line 2021-07-04 Answered

Transform the given differential equation or system into an equivalent system of first-order differential equations.
$\displaystyle{x}{''}+{2}{x}'+{26}{x}={82}{\cos{{4}}}{t}$

Which set of ordered pairs could be generated by an exponential function?
A. (1, 1) (2, 1/2) (3, 1/3) (4, 1/4)
B. (1, 1) (2, 1/4) (3, 1/9) (4 1/16)
C. (1, 1/2) (2, 1/4) (3, 1/8) (4, 1/16)
D. (1, 1/2) (2, 1/4) (3, 1/6) (4, 1/8)

Furthermore why is it that \(\displaystyle{e}^{{x}}\) is used in exponential modelling? Why aren't other exponential functions used, i.e. \(\displaystyle{2}^{{x}}\), etc?

What is the difference between linear growth and exponential growth?

Find the derivative of \(\displaystyle{y}={e}^{{{5}{x}}}\)

Solve \(\displaystyle{e}^{{{x}}}={0}\)

Differentiate, please: \(\displaystyle{y}={x}^{{{x}}}\).

Determine whether the given function is linear, exponential, or neither. For those that are linear functions, find a linear function that models the data. for those that are exponential, find an exponential function that models the data. xg(x) -12 05 18 211 314

James rents an apartment with an initial monthly rent of $1,600. He was told that the rent goes up 1.75% each year. Write an exponential function that models this situation to calculate the rent after 15 years. Round the monthly rent to the nearest dollar.

Find The Exponential Function \(\displaystyle{f{{\left({x}\right)}}}={a}^{{x}}\) Whose Graph Is Given.

Graph each function and tell whether it represents exponential growth, exponential decay, or neither. \(\displaystyle{y}={\left({2.5}\right)}^{{{x}}}\)

Transform the given differential equation or system into an equivalent system of first-order differential equations.
\(\displaystyle{x}{''}+{2}{x}'+{26}{x}={82}{\cos{{4}}}{t}\)

Exponential function questions and answers