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katovenus [111]

3 years ago

7

A certain quantity decays exponentially over time. The initial quantity at t = 0 is 1,000. The quantity decays at a rate of 2%.

What is the quantity at t = 4?

2 answers:

PtichkaEL [24]3 years ago

6 0

A=1000(1-0.02)^4
A==922.37

n200080 [17]3 years ago

4 0

Its D according to edgenuity.

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Please help me with the below question.

VMariaS [17]

By letting

$y = \displaystyle \sum_{n=0}^\infty c_n x^{n+r}$

we get derivatives

$y' = \displaystyle \sum_{n=0}^\infty (n+r) c_n x^{n+r-1}$

$y'' = \displaystyle \sum_{n=0}^\infty (n+r) (n+r-1) c_n x^{n+r-2}$

a) Substitute these into the differential equation. After a lot of simplification, the equation reduces to

$5r(r-1) c_0 x^{r-1} + \displaystyle \sum_{n=1}^\infty \bigg( (n+r+1) c_n + (n + r + 1) (5n + 5r + 1) c_{n+1} \bigg) x^{n+r} = 0$

Examine the lowest degree term $\left(x^{r-1}\right)$ , which gives rise to the indicial equation,

$5r (r - 1) + r = 0 \implies 5r^2 - 4r = r (5r - 4) = 0$

with roots at r = 0 and r = 4/5.

b) The recurrence for the coefficients $c_k$ is

$(k+r+1) c_k + (k + r + 1) (5k + 5r + 1) c_{k+1} = 0 \implies c_{k+1} = -\dfrac{c_k}{5k+5r+1}$

so that with r = 4/5, the coefficients are governed by

$c_{k+1} = -\dfrac{c_k}{5k+5} \implies \boxed{g(k) = -\dfrac1{5k+5}}$

c) Starting with $c_0=1$ , we find

$c_1 = -\dfrac{c_0}5 = -\dfrac15$

$c_2 = -\dfrac{c_1}{10} = \dfrac1{50}$

so that the first three terms of the solution are

$\displaystyle \sum_{n=0}^2 c_n x^{n + 4/5} = \boxed{x^{4/5} - \dfrac15 x^{9/5} + \frac1{50} x^{13/5}}$

4 0

1 year ago

A quantity with an initial value of 8600 grows exponentially at a rate of 20% every 2 minutes. What is the value of the quantity

Hatshy [7]

Answer:

23400 x 8/100 = 1872 = the loss

1872 : 12 = 156= the loss each month

156/1872*100% = 8.33 % then round it

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3 years ago

What is 26 1/2 divided by 6 5/8??

mariarad [96]

The answer is 4 So yeaaaa....

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3 years ago

Nina's net income was $423.65,and her gross income was $558.What was the total amount of deductions?

kompoz [17]

Gross=amount earned not minusing tax
net=amount earned minus tax

gross=558
net=423.65

deduction=gross-net
deduction=558-423.65=134.35

deduction=$134.35

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What's the pattern of 160,80,40,20,10

Brrunno [24]

The pattern is that each number is decreasing by half

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