Answered: Convert the equation f(t)=234(0.92)^t…

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter5: Inverse, Exponential, And Logarithmic Functions

Section5.3: The Natural Exponential Function

Problem 44E

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The half-life of plutonium-244 is 80,000,000 years. Find function gives the amount of carbon-14 remaining as a function of time, measured in years.
If a coffee filter is dropped, its velocity after t seconds is given by v(t)=4(10.0003t) feet per second. What is the terminal velocity, and how long does it take the filter to reach 99 of terminal velocity? Use a table increment of 0.1 and given your answer to the nearest tenth of a second.
The kinetic energy E of an object varies jointly with the object’s mass m and the square of the object’s velocity v . An object with a mass of 50 kilograms traveling at 16 meters per second has a kinetic energy of 6400 joules. What is the kinetic energy of an object with a mass of 70 kilograms traveling at 20 meters per second?
If xis large, which function grows faster, f(x)=2x or g(x)=x2?
The value of a car decreases each year. The rate at which the value decreases is called depreciation and is a represented by a percentage. For Alina buys a car for $25,000, and the depreciation rate is 25%. That means that her car’s value goes down by 25% each year. The value can be represented by the function V(y)=25000(0.75)^v, where V represents the value of her car and y represents the number of years that she owns a car. Find the depreciated value of her car if she keeps it for 5 years. In other words, evaluate: V(5)=25000(0.75)^5, rounding to the proper decimal place for money.
A person leans over a cliff that is 2000 feet high and throws a rock vertically upward at a speed of 100 ft/sec. When it falls, it barely misses the cliff and falls on the ground at the base of the cliff. The height of the rock (in feet) above the ground t seconds after it was thrown is given by the function f(t) = -16^2 + v0t + s0 where v0 is the initial velocity of the rock and so is the original height of the rock. Therefore f(t)=-16t^2+100t+2000. Determine when the rock will hit the ground at the base of the cliff. What was the maximum height of the rock?
For the function y=inx, find f(e^2)
Find f"(x).
Solve for the 4th derivative of function K K= x3Cos√x
The function e(m) represents the elevation above sea level in feet of the Mississippi river a distance m miles from the headwaters in Minnesota.(a) What are the units of e'(m)? (b) Is e'(m) positive or negative? Explain why in a brief sentence. (c) The Mississippi river reaches its river delta after 2320 miles in the Gulf of Mexico. The delta, which is entirely at sea level, extends for at least 10 miles more into the Gulf of Mexico. What is e'(2325)? Explain why in a brief sentence.
A medication was administered and the function is, N(t) = 200 (0.85)^(t-1), which represents the amount of effective medication available after each hour since the medication was given. ("t - 1", is included in the formula since it takes one hour for the medication to be absorbed in the bloodstream). If each hour a drug is only 85% effective as previous hour, in time another dose will need to be given. How long will it take for the initial dose to reach a low level of 50 milligrams? Identify the independent and dependent variables.
Calculate derivative F(x) = (7-10x) (7+10x) by expanding or simplifying the function df/dx

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Convert the equation f(t)=234(0.92)^t to the form f(t)=ae^kt