A population of 640 bacteria is introduced into a culture and grows in number according to the equation , where t is measured in hours. Find the rate at which the population is growing when t = 6. Round your answer to two decimal places. ​

Solve the problem.A box with an open top is formed by cutting squares out of the corners of a rectangular piece of cardboard and then folding up the sides. If x represents the length of the side of the square cut from each corner, and if the original piece of cardboard is 14 inches by 13 inches, what size square must be cut if the volume of the box is to be 168 cubic inches?

For the given functions f and g, find the requested composite function value.f(x) = , g(x) = 2x;Find (f ∘ g)(3).

Form a polynomial whose zeros and degree are given. Use a leading coefficient of 1. Zeros: 2, multiplicity 2; 5, multiplicity 1; degree 3

Find the real solutions of the equation.x3 + 2×2 – 5x – 6 = 0

For the polynomial, list each real zero and its multiplicity. Determine whether the graph crosses or touches the x-axis at each x -intercept.f(x) = 3(x2 + 5)(x – 6)2

Decide whether the composite functions, f ∘ g and g ∘ f, are equal to x.f(x) = , g(x) = 4x + 5

The function f is one-to-one. Find its inverse.f(x) = x2 – 4, x ≥ 0

Use the Factor Theorem to determine whether x – c is a factor of f(x).f(x) = x3 + 6×2 – 14x + 16; x – 8

Use the following confusion matrix for the next 3 questions: Given this confusion matrix for a 3-class problem (dog, cat, mouse):   Dog Cat Mouse Dog 4 0 0 Cat 2 2 0 Mouse 0 0 2