Question

solve the following variation: interest varies jointly with time and principle of the interest is 1,000 when the time is 10 years and the principle is 6,000. then find the equation of the variable

Answer 1

`I\text{ = }(tP)/(60)`

Step-by-step explanation:

Interest varies jointly with time and principle

let I = interest

time = t

Principle = P

Mathematically:

`\begin{gathered} I\text{ }\alpha\text{ tP} \\ I\text{ = ktP} \\ where\text{ k = constant of proportionality} \end{gathered}`

when interest = 1000

time = 10 years

Principal = 6000

We will substitute these values in the formula we got above to get k:

`\begin{gathered} 1000\text{ = k}*10*6000 \\ 1000\text{ = 60000k} \\ divide\text{ both sides by 60000:} \\ (1000)/(60000)\text{ = }(60000k)/(60000) \\ k\text{ = 1/60} \end{gathered}`

To get the equation of the variable, we will substitute the value of k in the formula:

`\begin{gathered} I\text{ = }(1)/(60)* t* P \\ \\ Equation\text{ of the variable:} \\ I\text{ = }(tP)/(60) \end{gathered}`