# Math Help - Logarithmic function help

1. ## 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.

2. 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.

3. 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.

4. 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:

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

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

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

$20=1.076^t$

$\ln 20=t \ln 1.076$

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