SOLUTION: 1. If $4000 is deposited into an account paying 3% interest compounded annually and at the same time $2000 is deposited into an account paying 5% interest compounded annually, afte
Algebra.Com
Question 70181: 1. If $4000 is deposited into an account paying 3% interest compounded annually and at the same time $2000 is deposited into an account paying 5% interest compounded annually, after how long will the two accounts have the same balance? Round to the nearest year and show all work.
2. Would you prefer that your salary be modeled exponentially or logarithmically? Explain your answer
3. If the half-life of a radioactive substance is 45 minutes and you originally have 2500 grams of the substance, how much will be left after 3 hours? Explain how to determine the amount without using the exponential model.
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
1. If $4000 is deposited into an account paying 3% interest compounded annually and at the same time $2000 is deposited into an account paying 5% interest compounded annually, after how long will the two accounts have the same balance? Round to the nearest year and show all work.
--------------
4000(1+0.03)^t = 2000(1+0.05)^t
2000=[(1.05)^t]/[1.03]^t
2000= [1.019417478]^t
Take the log of both sides to get:
t=(log2000/log1.019417478]
t=395.23 yrs.
---------
2. Would you prefer that your salary be modeled exponentially or logarithmically? Explain your answer
Y=ab^x is an increasing function so long as a and b are positive
and x represents successive years.
y=log x is also an increasing function but increases much more
slowly than the exponential fuction.
-------------
3. If the half-life of a radioactive substance is 45 minutes and you originally have 2500 grams of the substance, how much will be left after 3 hours? Explain how to determine the amount without using the exponential model.
A(t)=2500(1/2)^(t/45) where t is minutes elapsed
3 hrs is 180 minutes
A(180)= 2500(1/2)^(180/45)
=2500(1/2)^4
=2500/16
=156.25 grams
Cheers,
Stan H.
RELATED QUESTIONS
if $4000 is deposited into an account paying 3% interest compounded annually and at the... (answered by Alan3354)
If $4000 is deposited into an account paying 3% interest compounded annually and at the... (answered by rfer)
$500 was deposited on January 1, 1980, in an account paying 12% compounded semi-annually. (answered by stanbon)
If $9,000.00 is deposited into an account paying 4% interest compounded annually (at the... (answered by stanbon)
Can someone help me with this problem?
If $7,800 is deposited into an account paying (answered by psbhowmick)
What is the algebra formula if I invest into an ordinary annuity where $1100 is deposited (answered by Theo)
If 5,600 is deposited into an account paying 5% interest compounded annually, (at the end (answered by stanbon)
Find the final amount of money in an account if P3 ,500
is deposited at 3% interest... (answered by mananth,MathTherapy)
I am having a diffcult time finding the correct anser to the following question.
How... (answered by John10,solver91311)