the simple interest received from investment is directly proportional to the amount of the investment. By investing $4000 in a municipal bond you obtain interest of $280 at the end of 1year. Find a mathematical model that gives the interest I at end of 1year in terms of the amount P.

Let x=interest,

4000:280 = P : x

converts into the equation

4000/280 = P / x
which when cross multiplied gives
4000x = 280P
divide both sides by 4000 to get:
x(interest) = (280/4000)P
=(7/100)P
or
=0.07P

To find the mathematical model that gives the interest I at the end of 1 year in terms of the amount P, we can use the concept of proportionality.

From the given information, we know that the simple interest received is directly proportional to the amount of the investment. This means that the ratio of the interest to the principal investment remains constant.

Let's use k as the constant of proportionality. According to the given information:

I / P = k

We can substitute the given values into the equation:

280 / 4000 = k

Simplifying:

0.07 = k

Now that we have the value of k, we can rewrite our equation:

I = k * P

Substituting the value of k:

I = 0.07 * P

Therefore, the mathematical model that gives the interest I at the end of 1 year in terms of the amount P is:

I = 0.07P

To find a mathematical model that gives the interest "I" at the end of 1 year in terms of the amount invested "P," we can use the information given in the question.

The question states that the simple interest received from an investment is directly proportional to the amount of the investment. This means that the ratio of the interest to the investment amount is constant.

Let's consider the given values:

Amount of investment, P = $4000
Interest received at the end of 1 year, I = $280

We can set up the proportion by dividing the interest by the investment amount:

I / P = k

Where k is the constant of proportionality.

Now, plug in the values we have:

280 / 4000 = k

Simplifying the equation:

0.07 = k

So, the constant of proportionality is 0.07.

Now, we can rewrite the equation in terms of P and solve for I:

I / P = 0.07

Cross-multiplying:

I = 0.07P

Therefore, the mathematical model that gives the interest "I" at the end of 1 year in terms of the amount invested "P" is:

I = 0.07P