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.
|
|
|
