Charlie, who is 5 feet tall, walks away from a streetlight that is 16 feet high at a rate of 6 feet per second, as shown in the figure. express the length s of charlie's shadow as a function of time. (hint: first use similar triangles to express s as a function of the distance d from the streetlight to charlie.)

Given:

Height of Charlie: 5 feet 
Height of street light: 16 feet
Rate of movement: 6 feet/s

Illustrate the problem by drawing two similar triangles. The first leg of triangle 1, the height of the street light. The first leg of triangle 2, the height of Charlie. The shadow is moving at y ft/s. The distance between Charlie and the light is also moving at x ft/s.

The equation is y = $72.99 + $28.45(x - 1), where y is the monthly charge and x is the month in which it is calculated.

Step-by-step explanation:

Step 1; First we need to establish a relation between the difference in costs. For the first month it cost $72.99, during the second month, it costs $101.44 and in the third month, it costs $129.89. Difference in rates

Second months rate - First months rate = $101.44 - $72.99 = $28.45

Third months rate - Second months rate = $129.89 - $101.44 = $28.45.

So for every consecutive month, the charges increase by $28.45

Step 2; Now we develop an equation,

y = $72.99 + $28.45(x - 1), where y is the charge that month and x is the month in which it is calculated.

For x = 1, y = $72.99 + $28.45(1 - 1) = $72.99 + $28.45(0) = $72.99,

For x = 2, y = $72.99 + $28.45(x - 1) = $72.99 + $28.45(2 - 1) = $101.44,

For x = 3, y = $72.99 + $28.45(3 - 1) = $72.99 + $28.45(3-1) = $129.89.

So this is the equation to calculate the cost y the mobile provider charges in month x.