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nlexa [21]
3 years ago
15

Radioactive material disintegrates at a rate proportional to the amount currently present. If Q(t) is the amount present at time

t (in weeks), then dQ dt = −rQ, where r > 0 is the decay rate.
A) If 500 mg of a mystery substance decays to 83.01 mg in 5 weeks, determine the decay rate r.
B) Find an expression for the amount of this substance present at any time t.
C) Find the time required for the substance to decay to one-half its original amount.

Mathematics
1 answer:
stepladder [879]3 years ago
3 0

Answer:

Step-by-step explanation:

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2 years ago
Pls help if I don’t finish today mom will hurt me
kherson [118]

Answer:

We conclude that:

  • g(10) = 8

Step-by-step explanation:

First, we need to clear some concepts on how to fetch input and output from the function graph.

Determining the y-intercept:

We know that the y-intercept of the graph function can be determined by setting x = 0 and determining the corresponding y-value.

From the graph it is clear that x = 0, the value of y = 5. In other words, the graph intersects the y-axis at y = 5.

Therefore, the y-intercept of the graph is (0, 5).

Thus,

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Determining the x-intercept:

We know that the x-intercept of the graph function can be determined by setting y = 0 and determining the corresponding x-value.

From the graph, it is clear that y = 0, the value of x = -10. In other words, the graph intersects the x-axis at x = -10.

Therefore, the x-intercept of the graph is (-10, 0).

Thus,

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Determining g(10):

From the graph, it is clearly visible that at x = 10, the value of the function output y = 8.

In other words,

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Therefore, we conclude that:

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5 0
2 years ago
I'm confused<br>What is the answer?​
forsale [732]

If <em>c</em> > 0, then <em>f(x</em> - <em>c)</em> is a shift of <em>f(x)</em> by <em>c</em> units to the right, and <em>f(x</em> + <em>c)</em> is a shift by <em>c</em> units to the left.

If <em>d</em> > 0, then <em>f(x)</em> - <em>d</em> is a shift by <em>d</em> units downward, and <em>f(x)</em> + <em>d</em> is a shift by <em>d</em> units upward.

Let <em>g(x)</em> = <em>x</em>. Then <em>f(x)</em> = <em>g(x</em> + <em>a)</em> - <em>b</em> = (<em>x</em> + <em>a</em>) - <em>b</em>. So to get <em>g(x)</em>, we translate <em>f(x)</em> to the left by <em>a</em> units, and down by <em>b</em> units.

Note that we can also interpret the translation as

• a shift upward of <em>a</em> - <em>b</em> units, since

(<em>x</em> + <em>a</em>) - <em>b</em> = <em>x</em> + (<em>a</em> - <em>b</em>)

• a shift <em>b</em> units to the right and <em>a</em> units upward, since

(<em>x</em> + <em>a</em>) - <em>b</em> = <em>x</em> + (<em>a</em> - <em>b</em>) = <em>x</em> + (- <em>b</em> + <em>a</em>) = (<em>x</em> - <em>b</em>) + <em>a</em>.

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2 years ago
Write y=-3(x-7)^2-8 in vertex form
Veronika [31]

It's in the verex form:

f(x)+a(x-h)^2+k\\\\(h,\ k)-vertex

y=-3(x-7)^2-8\\\\(7,\ -8)-vertex

7 0
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