Question

Solve the following equation. For full marks your answer(s) should be rounded to the nearest cent.

x(1.03)3 + $105 + x1.032 = $4001.035

x = $0.00

Answer 1

x=$3059.00

Explanation:

To solve this equation, we need to use the properties of exponential functions and perform some algebraic manipulations. First, we can simplify the right-hand side of the equation by combining the constant terms and the exponent on the x:

$4001.035 = $105 + x(1.03)3 + x(1.032)

Next, we can combine the x terms on the left-hand side by multiplying them out and combining the exponents:

x(1.03)3 + x(1.032) = x(1.03)3 + x(1.03)(1.03) = x(1.03)4

Now we have:

$4001.035 = $105 + x(1.03)4

To solve for x, we need to isolate it on one side of the equation. We can do this by subtracting 105 from both sides:

$3900.035 = x(1.03)4

Next, we divide both sides by 1.03^4

x = $3900.035 / (1.03)^4

x = $3,059.00

x= $3059.00 (rounded to the nearest cent)