Consider the table representing an exponential function .

Using the table, the exponential function is given by:

An exponential function is modeled by:

From the table, when x = 0, y = 8, hence the value of coefficient a is

When x = 1, f(x) = y = 4, and this is used to find coefficient b.

Hence, using the values found for coefficients a and b, the function is defined by:

You can learn more about exponential functions at link

the ratio of balloons to tables is 5: 2 and the constant variation is 5.

the equation is y=5x

hello from mrbilldoesmath!

answer:

(7 x + 6 y) (49 x^2 - 42 x y + 36 y^2)

discussion:

the trick is to recognize that 343 = 7^3 and 216 = 6^3 and, in general,

a^3 + b^3 =   (a + b) (a^2 - a b + b^2).

in our case

343x^3+216y^3   =   (7x)^3 + (6y)^3

so take a = 7x and b = 6y in the above equation to get the answer.

you,

mrb