Answer:
28.23 days
Explanation:
Length of magic beanstalk=4 feet
Height increasing exponentially and double each day.
We have formula
[tex]y=a(b)^t[/tex]
Where t=Time (in day)
We have a=4
When t=1 then y=8
[tex]8=4b^1[/tex]
[tex]b=\frac{8}{4}=2[/tex]
[tex]b=2[/tex]
Distance between moon and earth=y=238,900 miles=[tex]238900\times 5280 feet[/tex]
Substitute the values
[tex]238900\times 5280=4(2)^t[/tex]
[tex]\frac{238900\times 5280}{4}=2^t[/tex]
[tex]315348000=2^t[/tex]
[tex]ln(315348000)=tln 2[/tex]
[tex]t=\frac{ln315348000}{ln 2}[/tex]
[tex]t=28.23 days[/tex]
