Question

Over time can be modeled by the equation v=20(1.05)t v = 20 ( 1.05 ) t , where v is the value of the coin in dollars and t is the number of years that have passed since chen bought the coin. what does the number 20 in the equation represent? responses the percent that the value of the coin increases each year the percent that the value of the coin increases each year the amount that chen paid for the coin the amount that chen paid for the coin the dollar amount that the value of the coin increases each year

Answer 1

The number 20 in the equation v=20(1.05)^t represents the initial amount paid for the coin, not the annual percent increase or the annual dollar increase.

Step-by-step explanation:

The equation v=20(1.05)^t represents the value of a coin over time with compounding interest.

In this context, the number 20 signifies the initial value or the amount that Chen paid for the coin when he first bought it.

It does not represent the percent increase each year nor the dollar amount by which the coin's value increases each year.

Those concepts are captured by the factor (1.05)^t, where 1.05 indicates a 5% annual increase in the coin's value.

Hence, the number 20 in the equation v=20(1.05)^t represents the initial amount paid for the coin, not the annual percent increase or the annual dollar increase.