(1) The amount of garbage, G, produced by a city with population p is given by $G = f(p)$. G is measured in tons per week, and p is measured in thousands of people.

The town of Tola has a population of 65,000 and produces 16.50 tons of garbage each week.

Express this information in terms of the function f:

$f(68) = 1.50$

Explain the meaning of the statement $f(1) = 4.90$:

This statement means that a city with a population of 1,000 people produces 4.90 tons of garbage per week.

(2) Let $f(t)$ be the number of ducks in a lake $t$ years after 1990. Explain the meaning of each statement:

$f(9) = 30$

This statement means that in the year 1990 + 9 = 1995, there were 30 ducks in the lake.

$f(§§V9(9 + 1, 20, 1)§§) = §§V10(30 + 5, 60, 1)§§$

This statement means that in the year 1990 + §§V9(9 + 1, 20, 1)§§ = §§V11(1995 + 1, 2010, 1)§§, there were §§V10(30 + 5, 60, 1)§§ ducks in the lake.

(3) Let $h(t)$ be the height above ground, in feet, of a rocket $t$ seconds after launching. Explain the meaning of each statement:

$h(5) = 170$

This statement means that 5 seconds after the rocket was launched, its height above the ground was 170 feet.

$h(§§V14(5 + 1, 10, 1)§§) = §§V15(170 + 50, 400, 10)§§$

This statement means that §§V14(5 + 1, 10, 1)§§ seconds after the rocket was launched, its height above the ground was §§V15(170 + 50, 400, 10)§§ feet.

(4) The number of cubic yards of dirt, D, needed to cover a garden with area a square feet is given by $D = g(a)$.

A garden with area 3500 ft² requires 25 $yd^3$ of dirt. Express this information in terms of the function g:

$g(3500) = 25$

Explain the meaning of the statement $g(170) = 2.50$:

This statement means that a garden with an area of 170 square feet requires 2.50 cubic yards of dirt to be covered.

(5) Show that the function $f(x) = 3(x - -5)^2 + 7$ is not one-to-one.

To show that the function $f(x) = 3(x - -5)^2 + 7$ is not one-to-one, we need to find two different values of $x$ that produce the same value of $f(x)$.

Consider $x_1 = -5 + 3$ and $x_2 = -5 - 3$. Since 3 is a positive integer, $x_1 \neq x_2$.

Now let's evaluate $f(x_1)$ and $f(x_2)$: $f(x_1) = 3((-5 + 3) - -5)^2 + 7 = 3(3)^2 + 7 = 3 \cdot 14 + 7 = 75 + 7$

$f(x_2) = 3((-5 - 3) - -5)^2 + 7 = 3(-3)^2 + 7 = 3(3)^2 + 7 = 3 \cdot 14 + 7 = 75 + 7$

Since $f(x_1) = f(x_2)$ but $x_1 \neq x_2$, the function $f(x) = 3(x - -5)^2 + 7$ is not one-to-one. This is because it's a quadratic function, and parabolas are symmetric around their vertex.