Find the values of y = c(x) = for x = 0, 0.008, 0.027, 0.064, 0.125, 0.216, 0.343, 0.512, , 0.729, and 1.

c(x) is a function, then we will solve the problem for two different functions.

1. If

Then

Using each of the values for x we have.

When x=0 the result is:  

When x=0.008 the result is:

When x=0.027 the result is:

When x=0.064 the result is:

When x=0.125 the result is:

When x=0.216 the result is:

When x=0.343 the result is:

When x=0.512 the result is:

When x=0.729 the result is:

When x=1 the result is:

2. If

Then

Using each of the values for x we have.

When x=0 the result is:  

When x=0.008 the result is:

When x=0.027 the result is:

When x=0.064 the result is:

When x=0.125 the result is:

When x=0.216 the result is:

When x=0.343 the result is:

When x=0.512 the result is:

When x=0.729 the result is:

When x=1 the result is:

step-by-step explanation:

the answer is 128

the solution of the equation is 2.23 ⇒ answer b

step-by-step explanation:

* lets revise the meaning of exponential function

- the form of the exponential function is y = ab^x, where a ≠ 0, b > 0 ,  

  b ≠ 1, and x is any real number

- it has a constant base b

- it has a variable exponent x

- to solve an exponential equation, take the log or ln of both sides,  

  and solve for the variable

* lets solve the problem

∵

- the base is 7 and the exponent is x

- insert ㏑ in both sides

∴

- use the rule

∴ x ㏑(7) = ㏑(77)

- to find x divide both sides by ㏑(7)

∴

* the solution of the equation is 2.23 to the nearest 2 decimal places