Question

Craig started the summer with 10 freckles. The number of freckles, F, has doubled each week, W, since summer began. Which equation represents the number of freckles Craig has since summer started?​

Answer 1

Answer:
`\bold{D)\quad f = 10(2)^w}`

Explanation:

"doubled each week" is a hint that this is an exponential equation.

Exponential equation is of the form: y = a(b)ˣ where

• "a" is the initial value (starting point)
• "b" is the rate of increase (or decrease)

It is given that Craig started the summer with 10 freckles → a = 10

It is given that the freckles doubled each week → b = 2

Input the "a" and "b" values to get: y = 10(2)ˣ

If you substitute "f"(freckles) for y and "w" (week) for x, then you get option D

`\large\boxed{\bold{D)\quad f=10(2)^w}}`

Answer 2

The answer to your question is letter D

Explanation:

Letter A. It is not possible because it is necessary to considers the variable (number of weeks)and this option does not consider it.

Letter B. It is not possible besides it consider the number of weeks the results do not correspond with the conditions given.

Example: for week 1, the number of freckles is 10 + 2¹ = 10 + 2 = 12, and the number of freckles must be 20.

Letter C. It is incorrect because the numbers of freckles do not correspond with the conditions.

Example: week 2 f = 2(10) ² = 2(100) = 200, it is higher than the expected.

Letter D. This is the correct answer because it satisfied the conditions given.