Mathematics, 02.07.2019 10:20 cecilf57p2rpuf

Tom invests $10,000 in a savings account that offers 3.5 percent interest, compounded continuously. in 10 years tom will have earned $(blank) in interest, and in (blank) years the investment will double. (use the rule of 70 where required.)

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Answer from: briabrodnax19

Compound interest formula

$A=P(1+ \frac{r}{n} )^{nt}$

Where

A= Future value
P = the Principal (the initial amount of money)
r = annual interest rate

t = time

n= number of times compounded in one t

Remark
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r is generally a percentage like 3%, 7% etc and are applied in the formula as 0.03, 0.07...,

the interest is compounded generally annually (n=1), quarterly (n=4), monthly (n=12), etc...

t is in years,

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Compounding continuously means that n tends (or goes) to infinity.

As n goes to infinity, the expression $P(1+ \frac{r}{n} )^{nt}$ is:

$\displaystyle{ \lim_{n\to\infty}P(1+ \frac{r}{n} )^{nt}=Pe^{rt}$

where e = 2.718.... (I assume this is rule 70)
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In short, when n is infinite, that is when we compound continuously, the formula is :

$A=Pe^{rt}$ ,

for P=$10,000, r=3.5/100=0.035, and t=10 years, we have:

$A=Pe^{rt}=\displaystyle{ 10,000\cdot e^{0.035\cdot10}=14,190.7$

dollars.

To perform the last equation we make use of a scientific calculator.

$14,190.7

Answer from: Quest

i think 5 miles per hour

step-by-step explanation:

Answer from: Quest

answer: a video game has three difficulty levels: easy, medium, and expert. the game's scoring works in such a way that a player has to score a fixed number of points to advance to the next level, and then the scoring starts over. the total score needed to clear all three difficulty levels is 7,500. two times the number of points needed to clear the easy level is 500 more than the number of points needed to clear the medium level. twice the number of points needed to clear the medium difficulty level is 1,500 more than the number of points needed to clear the expert level. if x, y, and z represent the easy, medium, and expert levels, respectively, and a is the coefficient matrix of the system of equations modeling this situation, identify the inverse matrix, a-1, and the solution matrix, x, of the system of equations.

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