The amount of money, in dollars, in a savings account after x years is given by M(x) = 10,000(1.03)x. What does the value 1.03 represent?
A) The original deposit was $103.
B) There is a 3 percent increase in the savings account each year.
C) The savings account earns $103 interest per month.
D) There is a 103 percent increase in the savings account each year.
To understand what the value 1.03 represents in the equation M(x) = 10,000(1.03)x, we need to break down the equation and understand the different parts.
In this equation, M(x) represents the amount of money in the savings account after x years.
The formula M(x) = 10,000(1.03)x shows that the initial deposit amount is $10,000, and it is being multiplied by 1.03 raised to the power of x.
Now, let's consider the options:
A) The original deposit was $103: This is not correct, as the equation states that the original deposit amount is $10,000, not $103.
B) There is a 3 percent increase in the savings account each year: This is the correct interpretation. The 1.03 in the equation represents a 3 percent annual increase. When we raise 1.03 to the power of x (the number of years), we are applying this 3 percent increase for each year.
C) The savings account earns $103 interest per month: This is not correct. The equation does not mention anything about monthly interest or a fixed amount of $103.
D) There is a 103 percent increase in the savings account each year: This option is not correct either. The 1.03 does represent an increase, but it is a 3 percent increase (as mentioned in option B), not 103 percent.
Therefore, the correct answer is B) There is a 3 percent increase in the savings account each year.
Your equation should be
M(x) = 10,000(1.03)^x , where x is the number of years
to me it says, the interest rate is 3% per annum, compounded annually
which of the choices best matches that description ?