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erica [24]
3 years ago
7

Find the first, fourth, and eighth terms of the sequence. A(n)=-2 × 2^N-1

Mathematics
1 answer:
11111nata11111 [884]3 years ago
7 0
<span><span>an</span>=<span><span>(<span>−<span>2x</span></span>)</span><span>(<span>2<span>−1</span></span>)</span></span></span>Step 1: Divide both sides by n.<span><span><span>an</span>n</span>=<span><span>−x</span>n</span></span><span>a=<span><span>−x</span>n</span></span>Answer:<span>a=<span><span>−x</span><span>n</span></span></span>
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2 years ago
the half-life of strontium-90 is approximately 29 years. how much of a 500 g sample of strontium-90 will remain after 58 years​
Yuliya22 [10]

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<u>Step-by-step explanation:</u>

A = P_o\cdot e^{kt}\\\\\text{First, use the given information to find k:}\\\\\bullet A=\dfrac{1}{2}P_o\\\\\bullet k = unknown\\\\\bullet t=29\text{ years}\\\\\dfrac{1}{2}P_o=P_o\cdot e^{k(29)}\\\\\\\dfrac{1}{2}=e^{k(29)}\qquad divided\ both\ sides\ by\ P_o\\\\\\ln\bigg(\dfrac{1}{2}\bigg)=ln\bigg(e^{k(29)}\bigg)\qquad applied\ ln\ to\ both\ sides\\\\\\ln\bigg(\dfrac{1}{2}\bigg)=29k\qquad simplified-ln\ and\ e\ cancel\ out\\\\\\\dfrac{ln\bigg(\dfrac{1}{2}\bigg)}{29}=k\qquad divided\ 29\ from\ both\ sides\\\\\\-0.0239=k

\text{Now, use the following in the equation to solve for A:}\\\\\bullet A=unknown\\\bullet P_o=500\\\bullet k=-0.0239\\\bullet t=58\text{ years}\\\\A=500\cdot e^{(-0.0239)(58)}\\\\.\quad=500\cdot e^{-1.386}\\\\.\quad=125

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Step-by-step explanation:

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