Final answer:
The concentration of dye after 5 seconds, calculated using the function f(5) = -0.006(5)⁴ + 0.140(5)³ - 0.053(5)² + 1.79(5), is 21.375. so, option B is the correct answer.
Step-by-step explanation:
To find the concentration of dye after 5 seconds using the model f(x) = -0.006x⁴ + 0.140x³ - 0.053x² + 1.79x, we need to calculate f(5). We substitute x with 5 and follow the order of operations to evaluate the polynomial.
f(5) = -0.006(5)⁴ + 0.140(5)³ - 0.053(5)² + 1.79(5)
First, we evaluate the powers: f(5) = -0.006(625) + 0.140(125) - 0.053(25) + 1.79(5)
Then we perform the multiplications: f(5) = -3.75 + 17.5 - 1.325 + 8.95
Finally, we add the results: f(5) = 21.375
The concentration of dye after 5 seconds is 21.375, which corresponds to option B.
The concentration of dye after 5 seconds is 21.375.
The concentration of dye after 5 seconds can be found by substituting x = 5 into the given equation for f(x). So, f(5) = -0.006(5)^4 + 0.140(5)^3 - 0.053(5)^2 + 1.79(5). Simplifying this expression gives f(5) = 21.375. Therefore, the concentration of dye after 5 seconds is 21.375.