Mr. Hibbard found a magic penny which doubles in value every day. The expression .01⋅2x

Question

can be used to find the value of his coin where x is the number of days since Mr. Hibbard found the penny.



Mr. Hibbard realized after just 2 weeks the penny had become $163.84! How did he reach this solution

(1 point)
Responses

Mr. Hibbard substituted x=2 into the expression .01⋅2⋅2=163.48
Mr. Hibbard substituted x=2 into the expression point 0 1 times 2 times 2 is equal to 163 point 4 8

Mr. Hibbard substituted x=2 into the expression .01⋅22=163.48
Mr. Hibbard substituted x=2 into the expression point 0 1 times 2 squared is equal to 163 point 4 8

Mr. Hibbard substituted x=14 into the expression .01⋅214=163.48
Mr. Hibbard substituted x=14 into the expression point 0 1 times 2 to the 14th power is equal to 163 point 4 8

Mr. Hibbard substituted x=14 into the expression .01⋅2⋅14=163.48

Answer 1

To find the value of the penny after 14 days, we will use the expression \(0.01 \cdot 2^x\), where \(x\) is the number of days.

Since Mr. Hibbard realized after 2 weeks, that would correspond to \(x = 14\) (since 2 weeks = 14 days).

Now, substituting \(x = 14\) into the expression:

\[ 0.01 \cdot 2^{14} \]

Calculating \(2^{14}\):

\[ 2^{14} = 16384 \]

Now multiplying by \(0.01\):

\[ 0.01 \cdot 16384 = 163.84 \]

So, we see that:

\[ Mr. Hibbard substituted x=14 into the expression 0.01 \cdot 2^{14} = 163.84 \]

Thus, the correct response is:

Mr. Hibbard substituted x=14 into the expression .01⋅2^14=163.84.

Answer 2

I just realized this, but "Mr. Hibbard" is my Homeroom Teacher...
*facepalm*

Answer 3

No worries! It's quite common to see names and characters in problems that might remind us of real people in our lives, especially in a classroom setting. It can be a fun coincidence! If you have any more questions about math, your teacher, or anything else, feel free to ask!