Question

Show that the nested evaluation technique used for polynomials can also be applied to the evaluation of f(x) = 1.01e⁴ˣ - 4.62e³ˣ -3.11e²ˣ + 12.2eˣ -1.99 Rewrite the function in its nested form.

Answer 1

To rewrite the function in its nested form, factor out the largest common factor among the exponential terms and evaluate each exponent term separately.

Step-by-step explanation:

To rewrite the function in its nested form, we will factor out the largest common factor among the exponential terms. In this case, the largest common factor is eˣ. Factoring out this common factor, we get:

f(x) = eˣ(1.01e³ˣ - 4.62e²ˣ - 3.11eˣ + 12.2 - 1.99)

Now, we can evaluate each exponent term separately, starting with the highest power of e and working down:

f(x) = eˣ(1.01(eˣ)³ - 4.62(eˣ)² - 3.11(eˣ) + 12.2 - 1.99)