Mathematics, 04.08.2020 04:01 mandilynn22

Cesium-137 has a half-life of about 30 years. A) Find the annual decay rate and round final result to 4 decimal places. B) Find the continuous decay rate and round final result to 4 decimal places. C) How long will it take for a 10 gram sample to decay to 1 gram? Round to nearest year and interpret your result with a complete sentence. D) Complete this statement: as x goes to infinity, y goes to ___.

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Answer from: Damagingawsomeness2

0.02280.0231100 years0

Step-by-step explanation:

The exponential equation for the fraction remaining after x years can be written as ...

y = (1/2)^(x/30)

A) For x=1, the fraction remaining is ...

y = (1/2)^(1/30) ≈ 0.97716 = 1 - 0.0228

Of the original amount, 0.0228 decays each year.

B) The continuous decay rate is the natural log of the growth factor, so is ...

ln(0.97716) = -0.0231

The continuous decay rate is 0.0231 of the present amount (per year).

C) For y=.10 (1/10 of the original amount) we find x to be ...

.1 = .5^(x/30)

ln(.1) = (x/30)ln(.5) . . . . . take the natural log

30ln(0.1)/ln(0.5) = x ≈ 100 . . . years

It will take 100 years for a 10-gram sample to decay to 1 gram.

D) As x goes to infinity, y goes to zero.

The relationship between growth rate and growth factor is ...

growth factor = 1 + growth rate

When the growth rate is negative, it is called a decay rate.

Answer from: Quest

here the number -5 is all of the following except a rational number.

step-by-step explanation:

Answer from: Quest

Intersecting secant-tangent theorem states that if a tangent segment and a secant segment are drawn to a circle from an exterior point, then the square of the measure of the tangent segment is equal to the product of the measures of the secant segment and its external secant segment.so to break it down: 1. pq acts as the tangent and ps as the secant with an intersection at p.sr = 21rp = 3x + 3pq = 4x + 4following to equation: tangent squared = the two segments multiplied by each otherso (4x + 4) ^ 2 = (3x + 3) • (21) simplifies to 16x^2 - 31x - 47 = 0 or (16x - 47)(x + 1) x = -1 or x = 47/162. pq acts as the tangent and ps as the secant with an intersection at p (again! )sr = 16rp = xpq = 15(15) ^ 2 = 16 • x225 = 16xx = 225/163. the interesting chords are proportional to each other so a ratio is possible to set up: ap dp 10 3 + x = = —— = pc pb 8 xcross multiple to get 10x = (3 + x)(8)x = 12

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Cesium-137 has a half-life of about 30 years. A) Find the annual decay rate and round final result t...

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