Understanding Exponential Models: Equations and Examples

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

Line 2021-07-04

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

Reggie 2021-06-30

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.
$\begin{array}{cc} Time (hours) & Bacteria count (CFU/mL) \\ 0 & 37 \\ 4 & 47 \\ 8 & 63 \\ 12 & 78 \\ 16 & 105 \\ 20 & 130 \\ 24 & 173 \end{array}$
Use a graphing calculator to find an exponential curve $f (t) = a \times b^{t}$ that models the bacteria population t hours later.

Jaya Legge 2021-06-25

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.

$\begin{array}{cc} x & g (x) \\ - 1 & 6 \\ 0 & 1 \\ 1 & 0 \\ 2 & 3 \\ 3 & 10 \end{array}$

aortiH 2021-06-13

The table shows the annual service revenues R1 in billions of dollars for the cellular telephone industry for the years 2000 through 2006. Year 2000 2001 2002 2003 2004 2005 2006 R1 52.5 65.3 76.5 87.6 102.1 113.51 25.5
(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 $R 2 = 6 + 13 + 13, 9^{0.14} t$ . What is the difference in total service revenues between the two models for the years 2010 through 2015?

djeljenike 2021-06-13

Transform the single linear differential equation into a system of first-order differential equations.
$x^{″} - 3 x^{'} + 2 x = t^{2}$

abondantQ 2021-06-10

The exponential growth models describe the population of the indicated country, A, in millions, t years after 2006. Canada A=33.1e0.009t Uganda A=28.2e0.034t 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. The models indicate that in 2013, Ugandas

avissidep 2021-06-09

Transform the given differential equation or system into an equivalent system of first-order differential equations.
$t^{3} x^{(3)} - 2 t^{2} x^{″} + 3 t x^{'} + 5 x = \ln t$

sanuluy 2021-06-02

The table shows the populations P (in millions) of the United States from 1960 to 2000. Year 1960 1970 1980 1990 2000 Popupation, P 181 205 228 250 282
(a) Use the 1960 and 1970 data to find an exponential model P1 for the data. Let t=0 represent 1960. (c) Use a graphing utility to plot the data and graph models P1 and P2 in the same viewing window. Compare the actual data with the predictions. Which model better fits the data? (d) Estimate when the population will be 320 million.

Carol Gates 2021-05-26

Transform the given differential equation or system into an equivalent system of first-order differential equations.
$x^{(4)} + 3 x + x = e^{t} \sin 2 t$

glasskerfu 2021-05-19

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. $\begin{matrix} x & f(x) \\ −1−1 & 32 23 \\ 0 & 3 \\ 1 & 6 \\ 2 & 12 \\ 3 & 24 \end{matrix}$

alesterp 2021-05-17

Transform the given differential equation or system into an equivalent system of first-order differential equations.
$x^{(4)} + 6 x^{″} - 3 x^{'} + x = \cos 3 t$

Ayaana Buck 2021-05-08

Transform the given differential equation or system into an equivalent system of first-order differential equations.
$x^{(3)} - 2 x^{″} + x^{'} = 1 + t e^{t}$

fortdefruitI 2021-05-04

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

pedzenekO 2021-05-03

The data below give the number of bacteria, in millions, found in a certain culture.
Time (hours) 0 1 2 3 4
Bacteria 5 8 15 26 48
Find an exponential function that models the data.

When you are looking for exponential function questions and answers, there are at least six transformations that you must use. Some examples with detailed solutions can be found below. Think about exponential function questions to see what approaches have been used, depending on what question has been asked. It will help you to understand the way things can be explained either in words or with a help of a graph. Start with an exponential model equation and proceed from there by using samples. There are also exponential growth questions that will be helpful as you learn.

Calculus 1

Exponential Model Examples: Learn with Our Experts