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christinachavez081

01.09.2022

The time time for the Acorn to descends from 13 feet to 1 feet is 52.25 seconds

Step-by-step explanation:

Given as :

The initial height of acorn = 13 feet in air

The rate of its descends = r = 4.8 feet every seconds

The final height of acorn = 1 feet

Le the time period of its descends = t sec

According to question

final height of acorn after t sec= initial height of acorn × $(1-\dfrac{rate}{100})^{\textrm time}$

Or, 1 feet = 13 feet × $(1-\dfrac{r}{100})^{\textrm t}$

Or, 1 feet = 13 feet × $(1-\dfrac{4.8}{100})^{\textrm t}$

Or, $\frac{1}{13}$ = $(0.952)^{\textrm t}$

Or, 0.07693 = $(0.952)^{\textrm t}$

Taking log both side

Log 0.07693 = Log ( $(0.952)^{\textrm t}$ )

or, - 1.113 = t Log (0.952) ( from log property $Loga^{b} = b Loga$ )

Or, - 1.113 = t ( - 0.0213 )

∴ t = $\dfrac{1.113}{0.0213}$

I.e t = 52.25 sec

So , The descending time is t = 52.25 seconds

Hence The time time for the Acorn to descends from 13 feet to 1 feet is 52.25 seconds Answer

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