Final answer:
The equation that represents the simple interest relationship, where simple interest earned varies jointly with the rate of interest and the number of years, given that $18 is earned at a 3% interest rate over 1.5 years, is n = $400 × r × t.
Step-by-step explanation:
The simple interest formula is expressed as Simple Interest (I) = Principal (P) × Rate of Interest (r) × Time (t), where the principal is the amount of money borrowed or invested, the rate is the percentage of interest, and the time is how long the money is borrowed or invested.
In this case, the amount of simple interest earned (‘n’) varies jointly with the rate of interest (‘r’) and the number of years (‘t’), so we can write the relationship as n = k × r × t, where ‘k’ is the constant of proportionality (or principal in this context).
To find the equation that represents this relationship, we need to use the provided information: the simple interest earned is $18 when the rate of interest is 3% for 1.5 years. We can substitute these values into our formula to solve for ‘k’:
$18 = k × 0.03 × 1.5
Dividing both sides of the equation by (0.03 × 1.5) gives us the value of ‘k’:
k = $18 / (0.03 × 1.5) = $400
Therefore, the equation that represents the simple interest relationship is:
n = $400 × r × t