(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 55,000 and produces 13.50 tons of garbage each week.

Express this information in terms of the function f:

$f(23) = 11$

Explain the meaning of the statement $f(9) = 4.80$:

This statement means that a city with a population of 9,000 people produces 4.80 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:

$f(8) = 50$

This statement means that in the year 1990 + 8 = 1994, there were 50 ducks in the lake.

$f(§§V9(8 + 1, 20, 1)§§) = §§V10(50 + 5, 60, 1)§§$

This statement means that in the year 1990 + §§V9(8 + 1, 20, 1)§§ = §§V11(1994 + 1, 2010, 1)§§, there were §§V10(50 + 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:

$h(3) = 300$

This statement means that 3 seconds after the rocket was launched, its height above the ground was 300 feet.

$h(§§V14(3 + 1, 10, 1)§§) = §§V15(300 + 50, 400, 10)§§$

This statement means that §§V14(3 + 1, 10, 1)§§ seconds after the rocket was launched, its height above the ground was §§V15(300 + 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 9500 ft² requires 85 $yd^3$ of dirt. Express this information in terms of the function g:

$g(9500) = 85$

Explain the meaning of the statement $g(170) = 3.50$:

This statement means that a garden with an area of 170 square feet requires 3.50 cubic yards of dirt to be covered.

(5) Show that the function $f(x) = 3(x - 7)^2 + 20$ is not one-to-one.

To show that the function $f(x) = 3(x - 7)^2 + 20$ is not one-to-one, we need to find two different values of $x$ that produce the same value of $f(x)$.

Consider $x_1 = 7 + 4$ and $x_2 = 7 - 4$. Since 4 is a positive integer, $x_1 \neq x_2$.

Now let's evaluate $f(x_1)$ and $f(x_2)$: $f(x_1) = 3((7 + 4) - 7)^2 + 20 = 3(4)^2 + 20 = 3 \cdot 18 + 20 = 60 + 20$

$f(x_2) = 3((7 - 4) - 7)^2 + 20 = 3(-4)^2 + 20 = 3(4)^2 + 20 = 3 \cdot 18 + 20 = 60 + 20$

Since $f(x_1) = f(x_2)$ but $x_1 \neq x_2$, the function $f(x) = 3(x - 7)^2 + 20$ is not one-to-one. This is because it's a quadratic function, and parabolas are symmetric around their vertex.