Write a compound interest function to model the following situation. then, find the balance after the given number of years.
$17,400 invested at a rate of 2.5% compounded annually; 8 years

Compound interest function,

The amount when compounded annually after 8 years is $

Step-by-step explanation:

Topic: Compound Interest

To model the situation, we'll make use of the compound interest formula. The formula is as follows:

---- This is the compound interest function

Where

r = Rate = 2.5% = 0.025

n = Period = Annually = 1

t = Time = 8 years

P = Principal Amount = $17,400

A = Amount ---- This is the function we want to model

By Substitution, we have

Hence, the amount when compounded annually after 8 years is $ (Approximated)

something that characterises a right triangle is the fact that we may use pythagoras' theorem to find any one of its sides given that we have the length of the other two sides. here, we have the length of the hypotenuse, √(87) yd, and one other side, √(23) yd, thus we can easily find the length of the remaining side using pythagoras' theorem as defined below:

c^2 = a^2 + b^2, where c is the length of the hypotenuse, and a and b are the lengths of the other two sides.

thus, given that c = √(87) and a = √(23), we may substitute these into the formula we defined above to get:

c^2 = a^2 + b^2

(√87)^2 = (√23)^2 + b^2 (substitute c = √87 and a = √23 into the equation)

87 = 23 + b^2 (evaluate (√87)^2 = 87 and (√23)^2 = 23 - remember that the square root of a number, squared will equal that very same number)

64 = b^2 (subtract 23 from both sides)

√64 = b (take the square root of both sides)

8 = b (evaluate √64 = 8)

therefor, the length of the unknown leg in the right triangle is 8 yd (first answer).

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