Instructions:Select the correct answer.
1 answer:
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Answer:
The function that represents the mass of the sample after t days is .
The percentage rate of change per hour is of -2.46%.
Step-by-step explanation:
Exponential amount of decay:
The exponential amount of decay for an amount of a substance after t days is given by:
In which A(0) is the initial amount, and r is the decay rate, as a decimal.
Element X is a radioactive isotope such that its mass decreases by 59% every day. The experiments starts out with 390 grams of Element X.
This means, respectively, that
So
The function that represents the mass of the sample after t days is .
Hourly rate of change:
Decreases by 59% every day, which means that for 24 hours, the rate of change is of -59%. So
-59%/24 = -2.46%
The percentage rate of change per hour is of -2.46%.
Answer:
Γ = 15
Step-by-step explanation:
Given
f(x) = x² - 8x + Γ
with a = 1, b = - 8 and c = Γ , then
sum of zeros α + β = - = -
= 8
product of zeros = αβ = = Γ
Given α - β = 2 , then
(α - β)² = 2²
α² - 2αβ + β² = 4 → (1)
and
(α + β)² = 8²
α² + 2αβ + β² = 64 → (2)
Add (1) and (2) term by term
2α² + 2β² = 68 ( divide through by 2 )
α² +β² = 34
Substitute α² + β² = 34 into (1)
34 - 2αβ = 4 ( subtract 34 from both sides )
- 2αβ = - 30 ( divide both sides by - 2 )
αβ = 15
Now
αβ = Γ = 15
Thus
f(x) = x² - 8x + 15