Question

If the moon is directly over the beanstalk, how many days after the beanstalk was planted would the beanstalk reach the moon? (The moon is 238,900 miles from the earth, and there are 5,280 feet in 1 mile.)

Answer 1

Answer:

28.23 days

Explanation:

Length of magic beanstalk=4 feet

Height increasing exponentially and double each day.

We have  formula

$y=a(b)^t$

Where t=Time (in day)

We have a=4

When t=1 then y=8

$8=4b^1$

$b=\frac{8}{4}=2$

$b=2$

Distance between moon and earth=y=238,900 miles=$238900\times 5280 feet$

Substitute the values

$238900\times 5280=4(2)^t$

$\frac{238900\times 5280}{4}=2^t$

$315348000=2^t$

$ln(315348000)=tln 2$

$t=\frac{ln315348000}{ln 2}$

$t=28.23 days$