Question 1127058
S = the length of the side of the square.
A = the area of the square.


the formula for the area of a square is A = S^2.


the length of the side of the suare increased by 10 centimeters every second.


T = the number of seconds.


A) Write a formula that expresses the side length of the square in cm, s, in terms of the number of seconds t since the square started growing.


S = 10 * T



B)Write a formula that expresses the area of the square in cm2, A, in terms of the side length of the square in cm, s.


A = S^2


C)Write a formula that expresses the area of the square in cm2, A, in terms of the number of seconds t since the square started growing.


A = (10 * T) ^2 which can be simplified to A = 100 * T^2.


D)Suppose the function f determines the area of the square in cm^2 given a number of seconds t since the square started growing. Write a function formula for f.


f(T) = 100 * T^2


when T = 0, f(0) = 100 * 0^2 = 0


this is derived as follows:


A = S^2
S = 10 * T
when T = 0, S = 10 * 0 = 0
when S = 0, A = 0^2 = 0


when T = 1, f(1) = 100 * 1^2 = 100


this is derived as follows:


A = S^2
S = 10 * T
when T = 1, S = 10 * 1 = 10
when S = 10, A = 10^2 = 100


when T = 2, f(2) = 100 * 2^2 = 100 * 4 = 400


this is derived as follows:


A = S^2
S = 10 *T
when T = 2, S = 10 * 2 = 20
when S = 20, A = 20^2 = 400


etc for all values of T