# Thread: Pre-test 6b Help Hurry

1. ## Pre-test 6b Help Hurry

questions are on attachment!!!

2. Hey Brookester:

Let's do #4. The bacteria.

What you need to do is use the given data and solve for k.

Once you know k, you can use that to solve the problem.

Given:

$\displaystyle 125=50e^{3k}$

Solve for k:

$\displaystyle \frac{5}{2}=e^{3k}$

$\displaystyle ln(\frac{5}{2})=3k$

$\displaystyle k=\frac{ln(\frac{5}{2})}{3}$

Now use that in the problem to solve. The initial population is 50. Triple that is 150.

$\displaystyle 150=50e^{\frac{ln(\frac{5}{2})}{3}t}$

$\displaystyle 3=e^{\frac{ln(\frac{5}{2})}{3}t}$

$\displaystyle ln(3)=\frac{ln(\frac{5}{2})}{3}t$

$\displaystyle t=\frac{3ln(3)}{ln(\frac{5}{2})}\approx{3.60}$

3. Hello, Brooke!

I believe we're suppose to use: $\displaystyle A \:= \:P\left(1 + \frac{i}{n}\right)^{nt}\quad\Rightarrow\quad P \;=\;\frac{A}{\left(1 + \frac{i}{n}\right)^{nt}}$

where $\displaystyle P$ is the principal investment,
$\displaystyle i$ is the annual interest rate,
$\displaystyle n$ is the number of compounding periods per year,
$\displaystyle t$ is the number of years.

2. An investment with an interest rate of 7% per annum yields $4000 in 3.5 years. What is the present value for each compounding period? . . A: annually . . B: semi-annually . . C: quarterly . . D: monthly (A) annually:$\displaystyle n = 1\displaystyle P \;= \;\frac{4000}{(1 + 0.07)^{3.5}} \;=\;3156.579774 \:\approx\; \$3,156.58$

(B) semi-annually: $\displaystyle n = 2$

$\displaystyle P \;= \;\frac{4000}{\left(1 + \frac{0.07}{2}\right)^{(2)(3.5)}} \;= \; 3143.963843 \:\approx\:\$3143.96\$

You can do the other two . . .
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