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# Exponential and logarithmic math problem?

A ring increases in value by 12% per year. In how many years, month, and days will it be four times its original amount?

### 5 Answers

- ?Lv 72 months ago
4= 1.12^t

ln4= tln1.12

t≈ 12.2325107... years or 372.112975... months or 4464.86640... days

- Pramod KumarLv 72 months ago
What do you mean by " increase in value" ? It can be increase in value of --

(1) its radius or (2) its Area, or even (3) its perimeter.

We will find that In any case, the result is same.

I am solving it for Radius,

Let the initial Value of Radius = R, so that after " t " years it increases to 4 R @ 12%

Applying Compound increase formula we get --

4 R = R ( 1 + 12/100 )^t

=> 4 = (1.12)^t

Taking log of both the sides we get --

=> log (4) = t log (1.12)

.... . . ... log (4). . . . . 0.60205999132796

=> t = --------------- = ----------------------------- = 12.232510748 years

. . . . . log (1.12) . . . .0. 04921802267018

=> t = 12 years-2 months-23.7 days. ............... Answer

- ?Lv 72 months ago
@Pramod Kumar

Ring - the kind that goes on a finger

A piece of jewelry that increases in value.

-------------------------------

Now as to the problem at hand:

4 = (1.12)^t

Take the log of both sides

log4 = t * log1.12

Divide both sides by log1.12

t = log4/log1.12

Use calculator

t = 12.23251074839941 years

12 years

.23251074839941years * 365.25 days/year = 84.9245508529 days

84.9245508529 days * 1mo/30.41667days = 2.7920397221 months

2 months

.7920397221 months * 30.41667days/month = 24.091210854 days

~ 24 days

Approximately,

12 years, 2 months and 24 days <––––––

(This could vary by a few days depending on how years and months are calculated)

From today: November 28, 2020

it would be February 21, 2033

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- David KLv 62 months ago
You cannot figure that exactly unless you define a specific start date. That is needed to ensure you account for explicit months (since they vary by number of days each). So I suggest you first figure the interest rate per day. Your class textbook should guide you the rest of the way.