Using an exponential function, it is found that the decay rate is of 6.24% a year.
<h3>What is an exponential function?</h3>
A decaying exponential function is modeled by:
![A(t) = A(0)(1 - r)^t](https://tex.z-dn.net/?f=A%28t%29%20%3D%20A%280%29%281%20-%20r%29%5Et)
In which:
- A(0) is the initial value.
- r is the decay rate, as a decimal.
The half-life is of 10.75 years, hence A(10.75) = 0.5A(0) and this is used to find the decay rate r.
![A(t) = A(0)(1 - r)^t](https://tex.z-dn.net/?f=A%28t%29%20%3D%20A%280%29%281%20-%20r%29%5Et)
![0.5A(0) = A(0)(1 - r)^{10.75}](https://tex.z-dn.net/?f=0.5A%280%29%20%3D%20A%280%29%281%20-%20r%29%5E%7B10.75%7D)
![(1 - r)^{10.75} = 0.5](https://tex.z-dn.net/?f=%281%20-%20r%29%5E%7B10.75%7D%20%3D%200.5)
![\sqrt[10.75]{(1 - r)^{10.75}} = \sqrt[10.75]{0.5}](https://tex.z-dn.net/?f=%5Csqrt%5B10.75%5D%7B%281%20-%20r%29%5E%7B10.75%7D%7D%20%3D%20%5Csqrt%5B10.75%5D%7B0.5%7D)
![1 - r = (0.5)^{\frac{1}{10.75}}](https://tex.z-dn.net/?f=1%20-%20r%20%3D%20%280.5%29%5E%7B%5Cfrac%7B1%7D%7B10.75%7D%7D)
1 - r = 0.9376.
r = 1 - 0.9376.
r = 0.0624.
The decay rate is of 6.24% a year.
More can be learned about exponential functions at brainly.com/question/25537936
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Answer:
(x-3)(x-9)
Step-by-step explanation:
first thing you need to do is move the -6 over. so we're going to add 6 to both sides (we add because it's negative 6 and we need 0 on the right side)
so you have: x^2-12x+27
now we need to come up with two numbers that add to -12 and multiply to 27.
the factors of 27 are 9 & 3 and 27 & 1. only 9 & 3 add to 12 so we are going to use those.
since the 12 is negative however, 9 and 3 should both be negative.
therefore we get: (x-3)(x-9)
*it doesn't matter which order you put them in!
Answer:
22miles
Step-by-step explanation:
Answer:
36 cm^3
Step-by-step explanation:
Area of right triangle ends 1/2 b * h = 1/2 * 3 * 4 = 6 cm^2
area * height = volume
6 x 6 = 36 cm^3
The least common multiple would be 209