The table below shows some input-output pairs for an exponential function g.>i. Determine the 1-unit scale (growth/decay) factor for g.Previewii. Determine the 1-unit percent g (i.e., express the scale factor as a percent).iii. Determine the 1-unit percent change for g.Previewg(x) =iv. Determine the initial value for g (the output value when the input is 0.)g(0) ==v. Write a function formula for9.X21g(x) 26.64 31.968PreviewPreview

We have a table .for With the help of this we find the required values

Answered: The table below shows some input-output…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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In a laboratory experiment, the population of bacteria in a petri dish started off at 3700 and is growing exponentially at 11% per day. Write a function to represent the population of bacteria after t days, where the hourly rate of change can be found from a constant in the function. Round all coefficients in the function to four decimal places. Also, determine the percentage rate of change per hour, to the nearest hundredth of a percent. Answer Attempt 4 out of 4 Function: f(t) = 3700(1+.11 Growth v (t/24) .11% increase per hour Submit Answer
b. The table below shows some input-output pairs for an exponential function g. i. Determine the 1-unit growth factor for g. * Preview ii. Determine the 1-unit percent change for g. = = g(0) iv. Write a function formula for g. g(x) X g(x) * Preview % iii. Determine the initial value for g (the output value when the input is 0.) * 篇 Preview 3 1 2 172.2 241.08 337.512 Preview Preview 5 661.52352
Health Services Expenditures The following tablegives total U.S. expenditures (in billions of dollars)for health services and supplies for selected yearsfrom 2000 and projected to 2018. a. Find an exponential function to model these data,with x equal to the number of years after 2000.b. Use the model to estimate the U.S. expendituresfor health services and supplies in 2020.
a. Consider the exponential function ƒ(x) = 54(0.38)ª. i. What is the initial value of f? f(0) = 54 ii. What is the 1-unit growth factor for f? 0.38 Preview % Preview iii. What is the 1-unit percent change for f? Preview
1 Given the following exponential function, identify whether the change represents growth or decay, and determine the percentage rate of increase or decrease. y=7900(1.05)^xy=7900(1.05)x 2 Find the equation of the exponential function represented by the table below: x y 0 0.1 1 0.3 2 0.9 3 2.7 y= 3 Write an exponential function in the form y=ab^xy=abx that goes through points (0, 9) and (3, 72)(
2. You bought a new computer for $2,500. Four years later, your computer is valued at $1,250. a. Assume that the cost function will be linear and write a linear function to describe the cost of the computer ?t years after you bought it. b. Assume that the cost function will be exponential (think of exponential decay) and write an exponential function to describe the cost of the computer ?t years after you bought it. c. For each function you just wrote, find the rate at which the cost is depreciating 3 years after you bought it. d. Which function do you think would be more accurate? Write a complete sentence or two describing why you think so.
Sunlight is absorbed in water, and as a result the light intensity in oceans, lakes, and ponds decreases exponentially with depth. The percentage of visible light -kx P (in decimal form) at a depth of x meters is given by P=e, where k is a constant related to the clarity and other physical properties of the water. The graph shows models for the open ocean, Lake Tahoe, and Lake Erie for data taken under similar conditions. Percent 0.8- 0.2- Percent of Surface Light vs. Depth -0.0491 x Ocean: P = e Tahoe: P = e -0.0799 x Depth (m) Erie: P = e -0.1980 x The euphotic depth for the open ocean is The euphotic depth is the depth at which light intensity falls to 1% of the value at the surface. This depth is of interest to scientists because no appreciable photosynthesis takes place. Find the euphotic depth for the open ocean. Round to the nearest tenth of a meter. meters. X

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