An artist creates a sculpture out of one ton of salt. If the sculpture loses 3.5% of its mass each year to erosion, after how long will the statue weigh less than 1,000 pounds?

using logarithms

Question

An artist creates a sculpture out of one ton of salt. If the sculpture loses 3.5% of its mass each year to erosion, after how long will the statue weigh less than 1,000 pounds?

using logarithms

justjm · Answer

let y be a function of x, where y is the weight in pounds and x is the time in years. We can depict the scenario through this relation:

$y=(1-0.035)^t$
$y=0.965^t$
You have to find how long until the statue weighs less than 1000 pounds.
$1000=0.965^t$
Solve by taking the natural log of each side and then using your log rules, then use your calculator.