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Crank
10 days ago
11

If dy/dt=-10e^-t/2 and y(0)=20 what is the value of y(6)​

Mathematics
1 answer:
lawyer [4K]10 days ago
3 0

RESPONSE

y (6)= \frac{20}{ {e}^{3} }

EXPLANATION

The equation provided is:

\frac{dy}{dt} = - 10 {e}^{ - \frac{t}{2} }

By integrating with respect to t, we obtain:

y = 20 {e}^{ - \frac{t}{2} } + k

The initial condition y(0)=20

We apply this initial condition to solve for:

20= 20 {e}^{ - \frac{0}{2} } + k

k = 0

This implies that;

y = 20 {e}^{ - \frac{t}{2} }

y (6)= 20 {e}^{ - \frac{6}{2} }

y (6)= 20 {e}^{-3}

Or

y (6)= \frac{20}{ {e}^{3} }

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Suppose that a student is randomly selected from a large high school. The probability that the student is a senior is 0.22. The
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3 0
5 days ago
The yearly cost in dollars, y, for a member at a video game arcade based on total game tokens purchased, x, is y =y equals Start
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Response:

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Given data:

Annual cost for members: y = \frac{1}{10}x + 6

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From the context, we infer that:

A non-member pays $0.20 per game;

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y = Amount * Number of Games

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13 days ago
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Answer:

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