SOLUTION: Exoponential Method 1.A biologist is researching a newly-discovered species of bacteria. at time t=0 hours, he puts one hundred bacteria into what he has determined to be a favora

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Question 393385: Exoponential Method
1.A biologist is researching a newly-discovered species of bacteria. at time t=0 hours, he puts one hundred bacteria into what he has determined to be a favorable growth medium. Six hours later, he measures 450 bacteria. Find an exponential equation thet approximates the information.
2. A $1,000 deposit is made at a bank that pays 12% compound monthly. How much will you havein your account at the end of 10 years.

Answer by ankor@dixie-net.com(22740) (Show Source):
You can put this solution on YOUR website!
1.A biologist is researching a newly-discovered species of bacteria.
at time t=0 hours, he puts one hundred bacteria into what he has determined to
be a favorable growth medium.
Six hours later, he measures 450 bacteria.
Find an exponential equation that approximates the information.
:
find k, the growth factor
100*(2^(6/k)) = 450
Divide both sides by 100
2^(6/k) = 4.5
use logs here
log(2^(6/k)) = log(4.5)
:
log(2) = log(4.5)
=
= 2.17
k =
k = 2.765 is the growth factor
:
A = Ao*2^(t/2.765), the exponential equation
where
Ao = initial amt
A = amt after t hrs
t = time in hrs
:
Check equation using Ao = 100: In a calc enter: 100*2^(6/2.765) results: 450.0
:
:
2. A $1,000 deposit is made at a bank that pays 12% compound monthly.
How much will you have in your account at the end of 10 years.
:
Compound interest formula:
A =
where
A = resulting amt after t years
P = principal ($1000)
r = interest rate in decimals (.12)
n = no. of time compounded per yr (12 times/yr)
t = no. of yrs (10 yrs)
:
A =
:
A =
:
A =
on a calc
A = $3300.39