Question

The first given value varies directly as the second given value. Find the constant of variation and write an equation of direct variation. An interest of $67.50 (t) is earned on a deposit of $1500 (p) over a year's time.

Answer 1

The constant variation for an interest of $67.50 on a $1500 deposit is 0.045 or 4.5%. Thus, t = 0.045p represents the direct variation of interest earned on the deposit.

Step-by-step explanation:

Direct Variation and Constant of Variation

To find the constant of variation when a value varies directly from another, we use the formula k = t / p, where t is the amount of interest earned and p is the principal deposit. In this case, an interest of $67.50 is earned on a deposit of $1500, so the constant of variation is $67.50 / $1500, which simplifies to 0.045 or 4.5%. Therefore, the direct variation equation representing this situation is t = kp, or, substituting in the constant, t = 0.045p.

An equation of direct variation represents the relationship whereas one quantity increases, another quantity increases at a constant rate. For instance, the amount of interest earned (t) increases in proportion to the principal (p) at a constant rate, which is the interest rate here. This is analogous to the provided example where a $100 deposit at a simple interest rate of 5% held for one year yields $5 in interest.