# Logarithmic function help

• Apr 25th 2010, 03:35 PM
danield3
Logarithmic function help
1. How long would it take for $25 to increase to$500 at 7.6% compounded annually? Round off your answer to the nearest year.

2. The population of a colony of bacteria doubles every 3 hours. How long, in hours, does it take for the population to be 3.5 times its original size? Answer correct to one decimal place.

3. Suppose the exponential model of a population growth is given by
P(t) = P010kt,
where P0 equals the original or initial population and t is time in hours. Find k, if a population of a culture is 540 now and is 2200 in 11 hours. (Accurate to 3 decimal places)

4. 210 grams of a radioactive substance decays to 80 grams after 880 years. To the nearest year, what is the half-life of the substance?

5. Earthquake intensity is given by I = Io(10)m, where Io is the reference intensity and m is magnitude. A particular major earthquake of magnitude 7.4 is 70 times as intense as a particular minor earthquake. The magnitude, to the nearest tenth, of the minor earthquake is

Logarithmic Applications Formula.

A = AO (B)^ T/P
A= Future Amount
Ao = Intial Amount
B = Type of growth
P = Period for Growth to occcur
T = Elaspsed Time.
• Apr 25th 2010, 10:04 PM
earboth
Quote:

Originally Posted by danield3
1. How long would it take for $25 to increase to$500 at 7.6% compounded annually? Round off your answer to the nearest year.

2. The population of a colony of bacteria doubles every 3 hours. How long, in hours, does it take for the population to be 3.5 times its original size? Answer correct to one decimal place.

3. Suppose the exponential model of a population growth is given by
P(t) = P010kt,
where P0 equals the original or initial population and t is time in hours. Find k, if a population of a culture is 540 now and is 2200 in 11 hours. (Accurate to 3 decimal places)

4. 210 grams of a radioactive substance decays to 80 grams after 880 years. To the nearest year, what is the half-life of the substance?

5. Earthquake intensity is given by I = Io(10)m, where Io is the reference intensity and m is magnitude. A particular major earthquake of magnitude 7.4 is 70 times as intense as a particular minor earthquake. The magnitude, to the nearest tenth, of the minor earthquake is

Logarithmic Applications Formula.

A = AO (B)^ T/P
A= Future Amount
Ao = Intial Amount
B = Type of growth
P = Period for Growth to occcur
T = Elaspsed Time.

Welcome on board!

You have (obviously) just started with exponential and logarithmic functions - right?

All your questions are standard exercises. So if you need some help you should show us what you have done so far and where you have difficulties to proceed.
• Apr 26th 2010, 10:48 AM
danield3
Quote:

Originally Posted by earboth
Welcome on board!

You have (obviously) just started with exponential and logarithmic functions - right?

All your questions are standard exercises. So if you need some help you should show us what you have done so far and where you have difficulties to proceed.

I have done some what on 1-4. And I do not know how to do it.

These are the answers for 1 -4
1. t=9.120357639
2.t=5.422064766
3. k=3.7%
4.r=0.10965%
5.?
I do not know if it is correct. So please tell me these right and help me in 5.
• Apr 26th 2010, 01:15 PM
masters
Quote:

Originally Posted by danield3
1. How long would it take for $25 to increase to$500 at 7.6% compounded annually? Round off your answer to the nearest year.

Hi danield3,

You might consider posting these one at a time and show as much detail as you can.

Your first one uses the compound interest formula:

$\displaystyle A=P\left(1+\frac{r}{n}\right)^{nt}$

A = amount of money accumulated after t years, including interest.

r = annual rate of interest (as a decimal)

t = number of years the amount is deposited or borrowed for.

n = number of times the interest is compounded per year

$\displaystyle 500=25\left(1+\frac{.076}{1}\right)^{1t}$

$\displaystyle 20=1.076^t$

$\displaystyle \ln 20=t \ln 1.076$

$\displaystyle t=\frac{\ln 20}{\ln 1.076} \approx 41$ years.