SOLUTION: In 1995, Ebenezer Bosticle created a salt sculpture that weighed 2,000 pounds. If this sculpture loses 4 percent of its mass each year to rain erosion, what is the last year in whi

Question 1189229: In 1995, Ebenezer Bosticle created a salt sculpture that weighed 2,000 pounds. If this sculpture loses 4 percent of its mass each year to rain erosion, what is the last year in which the statue will weigh more than 1,000 pounds?
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
In 1995, Ebenezer Bosticle created a salt sculpture that weighed 2,000 pounds.
If this sculpture loses 4 percent of its mass each year to rain erosion, what is the last year in which the statue will weigh more than 1,000 pounds?
:
If 4% is lost, 96% remains each year
let t = no. of years that 1000 lbs remain
2000*.96^t = 1000
.96^t = 1000/2000
.69^t = .5
using natural logs
t*ln(.96) = ln(.5)
t = ln(.5)/ln(.96)
using you calc
t = 16.98 yrs
round it down because you want it to be more than 1000
t = 16 yrs
1995 + 16 = 2011 is last yr over 1000 lb
:
Check this by finding the weight remaining after 16 yrs
2000*.96^16 = 1041 lbs after 16 yrs
and
2000*.96^17 = 999 lbs after 17 yrs
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