3. Dr. Silas studies the culture of bacteria under a microscope. The function b1(t) = 1200 (1.8)^t represents the number of bact
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A)
![\bf \qquad \qquad \textit{Future Value of an ordinary annuity} \\\\ A=pymnt\left[ \cfrac{\left( 1+\frac{r}{n} \right)^{nt}-1}{\frac{r}{n}} \right] \\\\](https://tex.z-dn.net/?f=%5Cbf%20%5Cqquad%20%5Cqquad%20%5Ctextit%7BFuture%20Value%20of%20an%20ordinary%20annuity%7D%0A%5C%5C%5C%5C%0AA%3Dpymnt%5Cleft%5B%20%5Ccfrac%7B%5Cleft%28%201%2B%5Cfrac%7Br%7D%7Bn%7D%20%5Cright%29%5E%7Bnt%7D-1%7D%7B%5Cfrac%7Br%7D%7Bn%7D%7D%20%5Cright%5D%0A%5C%5C%5C%5C)
B)
let's say after 12years, she ended up with a value of say "P"
so.. now she's just sitting on P, making no more deposits to it
just taking whatever the compound 5% interest will give, thus
C)
from A) she made 1,200 every year, for 12 years that's 1200*12, that's how much she put out of pocket, if you got an amount P from A), then the interest is just the difference, or P - (1200*12)
from B), she started with an original amount of P, and ended up with a compounded amount of A after 11years, so the interest is just also the difference, or A - P
add those two folks together, and that's the total interest she got for the 23 years
B)
let's say after 12years, she ended up with a value of say "P"
so.. now she's just sitting on P, making no more deposits to it
just taking whatever the compound 5% interest will give, thus
C)
from A) she made 1,200 every year, for 12 years that's 1200*12, that's how much she put out of pocket, if you got an amount P from A), then the interest is just the difference, or P - (1200*12)
from B), she started with an original amount of P, and ended up with a compounded amount of A after 11years, so the interest is just also the difference, or A - P
add those two folks together, and that's the total interest she got for the 23 years