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3 years ago

Scott invested $1,600 into a retirement account that earns 2.4% interest

Mathematics

1 answer:

Anit [1.1K]3 years ago

8 0

Answer:

A = $3294.73

Step-by-step explanation:

Use the compound amount formula:

A = P(1 + r/n)^(n*t), where n represents the number of compounding periods per year.

Here,

A = $1600(1 + 0.024/12)^(12*30)

= $1600*(1 + 0.002)^(12*30)

= $1600(1.002)^360

A = $3294.73

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If a substance decays at a rate of 25% every 10 years, how long will it take 512 grams of the substance to decay to 121.5 grams

Juliette [100K]

Answer:

It will take 50 years to decay from 512 grams to 121.5 grams.

Step-by-step explanation:

The decay formula :

$N=N_0e^{-\lambda t}$

where

N= amount of substance after t time

N₀= initial of substance

t= time.

A substance decays at a rate 25% every 10 years.

So, remaining amount of the substance is = (100%-25%)= 75%

$\frac{N}{N_0}=\frac{75\%}{100\%}=\frac{75}{100}=\frac34$ , t= 10

$N=N_0e^{-\lambda t}$

$\Rightarrow \frac {N}{N_0}=e^{-\lambda t}$

$\Rightarrow \frac34 =e^{-\lambda .10}$

Taking ln both sides

$\Rightarrow ln|\frac34| =ln|e^{-\lambda .10}|$

$\Rightarrow ln|\frac34|=-10\lambda$

$\Rightarrow \lambda=\frac{ ln|\frac34|}{-10}$

Now , N₀= 512 grams, N= 121.5 grams, t=?

$N=N_0e^{-\lambda t}$

$\therefore 121.5=512e^{-\frac{ln|\frac34|}{-10}.t}$

$\Rightarrow 121.5=512e^{\frac{ln|\frac34|}{10}.t}$

$\Rightarrow \frac{121.5}{512}=e^{\frac{ln|\frac34|}{10}.t}$

Taking ln both sides

$\Rightarrow ln|\frac{121.5}{512}|=ln|e^{\frac{ln|\frac34|}{10}.t}|$

$\Rightarrow ln|\frac{121.5}{512}|={\frac{ln|\frac34|}{10}.t}$

$\Rightarrow t=\frac{ln|\frac{121.5}{512}|}{\frac{ln|\frac34|}{10}}$

$\Rightarrow t=\frac{10.ln|\frac{121.5}{512}|}{{ln|\frac34|}}$

⇒t=50 years

It will take 50 years to decay from 512 grams to 121.5 grams.

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3 years ago

I need help for this..

IgorC [24]

Answer:

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Step-by-step explanation:

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2 years ago

If y = –0.96 when x = 2.4, what is y when x = 2.9?

Ksivusya [100]

Answer:

<u>It should be -1.16</u>

Step-by-step explanation:

Hope this helps :)

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1 year ago

Please help me with my math question!!!!

levacccp [35]

Answer:

No.

Step-by-step explanation:

It is because a line is said to be perpendicular to another line if the two lines intersect at a right angle or at 90° and the two lines in the graph does not intersect at 90° angle..

mark brianliest if my answer suit your question..

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3 years ago

Joel can either work 2 days for 11 hours each day or 4 days for 6 hours each day. He takes the bus for $2.25 each way. On days h

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