The penny size of a nail indicates the length of the nail. the penny size d is given by the literal equation d=4n−2, where n is the length (in inches) of the nail. a. solve the equation for n. n= question 2 b. use the equation from part (a) to find the lengths of nails with the following penny sizes: 3, 6, and 10. a 3-penny nail is inches. a 6-penny nail is inches. a 10-penny nail is inches.

The penny size d is given by the literal equation

Where n is the length (in inches) of the nail.

We can deduce the value of n from equation above:

Now we have to find n with various values of d.

1. when d = 3 inches

n = 1.25 inches

2. when d = 6 inches

n = 2 inches

3. when d = 10 inches

n = 3 inches

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