Question

Suppose James has a credit card with a balance of $4289. $ 4289 . Each month, the credit card company charges 5% 5 % interest. James pays off all new purchases that he makes each month without paying off the old balance or its interest. He wants to know what the balance on his credit card will be one year from now. Is this situation an example of exponential growth or exponential decay?

Answer 1

Answer:

balance in credit card = $4289

interest % = 5%

interest = P

T =P[ {1+\frac{r }{100}}]^n||

1=4289 [1+ \frac{5}{100} ]^ 1\\

i=4289[1+\frac{1}{20}]\\

|=4289 X \frac{21}{20}\\

I= $90258 /20

I = $4512.90

Answer 2

At the end of one year, his balance will be $ 4076.56 and this situation is an example of exponential growth.

Given:

Suppose James has a credit card with a balance of $4289 . Each month, the credit card company charges 5% interest. James pays off all new purchases that he makes each month without paying off the old balance or its interest.

To find:

He wants to know what the balance on his credit card will be one year from now. Is this situation an example of exponential growth or exponential decay?

Solution:

First we need to calculate the James monthly charges on his balance of 4289.

Using the simple interest formula;

Simple Interest = (Principal * Rate * Time)/100

Principal = 4289

Rate = 5%

Time = 1 month = 1/12 year

Simple interest = (4289*5*1/12)/ 100

Simple interest = 21,445/1200

Simple interest = 17.87

If monthly charge is 17.87, yearly charge will be 12 * 17.87 = 214.44

The balance on his credit card one year from now = Principal - Interest

= 4289 - 214.44

= 4076.56

The balance on his credit card one year from now will be $ 4076.56.

This is an example of exponential growth.

Quantity rises over time through a process called exponential growth. When a quantity's instantaneous rate of change with regard to time is proportionate to the quantity itself, it happens.

Here, interest is increasing in proportion to principal, hence it is an example of exponential growth.

Hence, the balance will be $4076.56 and this is exponential growth situation.

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