Question 19 Jon has a savings account that accumulates compound interest. The 4% annual interest rate is compounded 12 times a year. This function describes the relationship between the amount of money in the account and the number of years the account is allowed to grow.
A(t)=2000(1+0.0412)12t
Jon finds the value of A(12). Which quantity has he found?

A
the amount in the account after 12 years

B
the number of months the account has accumulated 4% interest

C
the amount in the account after 12 months

D
the number of years the account has accumulated 4% interest

When Jon determined A(12), it means he must have found the amount in the account after 12 years. i.e. the amount when t = 12 years.

Hence, option (A) is true.

Step-by-step explanation:

BACKGROUND KNOWLEDGE ABOUT EXPONENTIAL GROWTH

We know that an exponential increase in Math can be termed as the rapid increase of an amount by percentage over a certain period of time.

It can be expressed using the formula

y = a (1+b)ˣ

here

y represents the final amount

a represents the original amount

b represents the growth factor

x represents the time that has passed

Now, let is us map our problem because it indicates the same concept.

SOLVING THE QUESTION

Given the function

Here

A(t) represents the final amount

2000 represents the original amount

0.0412 represents the growth rate

t represents the number of years

Thus,

When Jon determined A(12), it means he must have found the amount in the account after 12 years. i.e. the amount when t = 12 years.

Hence, option (A) is true.

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