Question
Mr. Hibbard found a magic penny which doubles in value every day. The expression .01⋅2x
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
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
Answers
GPT-4o mini
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.**
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.**
I just realized this, but "Mr. Hibbard" is my Homeroom Teacher...
*facepalm*
*facepalm*
GPT-4o mini
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!