When a camera flash goes off, the batteries immediately begin to recharge the flash's capacitor, which stores electric charge given by q = q(t) = k(1 -tla). (The maximum charge capacity is k and t is measured in seconds). (a) Find the inverse of this function. (Explain its meaning.) (b) How long does it take to recharge the capacitor to 90 percent of capacity if a = 2? (a) t = \ (b) t = seconds [to the nearest tenth]

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Q: 12. f(x)=5-2/5x  express it in the form f(x) =ax+b and state the rate of change of the function.

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Q: (1) If you have been hired at an annual salary of $23,000 and expect to receive annual increases of…

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Q: The us population can be modeled by the function y=165.6x^1.345 where y is in thousands and x is the…

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Q: The following table gives for a certain man his height H= H(t) in inches at age t in years A- use…

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Q: If we put a cool object into a preheated oven, Newton's law of heating tells us that the difference…

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Q: 2. Let 10000 P(t) = 900e-t + 100 describe the size of a population at time t. Find the inverse…

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Q: Suppose we have a tank that contain 10 litres of water and 50 g of salt. The salt solution is…

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Q: The function f(x)=1+1.3 In (x+1) models the average number of free throws a basketball player can…

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A: Given: C = 743 − 0.402n + 0.00012n2 where,  C=per pupil cost n= the number of pupils enrolled To…

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Q: Does the function f(x) = 2e¯X represent exponential growth, decay, or neither? A) Exponential growth…

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Q: (a) A kitchen sink has a volume of 15 L. If the drain is closed and the sink is initially empty,…

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Q: The function f(x) = 1 + 1.4 ln (x+1) models the average number of free-throws a basketball player…

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A:

Q: A culture contains 2000 bacteria initially and doubles every 60 minutes. Assuming that the rate of…

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Q: Consider the function f(x) = i + x². How does this function essentially behave for large positive…

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Q: Find an equation of the line tangent to the graph of f(x) at the point (5,9): f(x) = e-3x-1o + 8

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Q: The life expectancy ℓ of white females can be estimated by using the function  ℓ(x) = 78.5(1.001)x,…

A: Given, life expectancy function lx=78.51.001x where x is the current age.

Q: Find the intervals of increase and decrease  for the function.   f(x)= ln(lnx-4)

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Q: In Example 2, we modeled the population size (in millions) of the United States as N(t) = 8.3(1.33)'…

A: The solution of above question no. #30 is written below with graph.

Q: The amount A (in g) remaining of a radioactive substance after time t (in years) is found by solving…

A:

Q: A culture contains 1400 bacteria initially and doubles every 50 minutes. Assuming that the rate of…

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Q: A culture contains 2000 bacteria initially and doubles every 40 minutes. Assuming that the rate of…

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Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.