1.) The Grand Canyon is 1600 meters deep at its deepest point. A rock thrown upw

Question

1.) The Grand Canyon is 1600 meters deep at its deepest point. A rock thrown upward at 11 meters per second and into the canyon from the rim above this point. Express the height of the rock as a function of the time t in seconds. How long will it take the rock to hit the canyon floor?

2.) Because of a slump in he economy, a conpany finds that its annual revenues have dropped from $742,000 in 2010 to $632,000 in 2012. If the revenue is following an exponential pattern of decline, what is the expected revenue for 2014? (Let t=0 represent 2010)

Explanation / Answer

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we need to find the exponential decay constant, k

632000=742000*e^kt, where t=2, solve for k,

(632000/742000)=e^2k

take ln of both sides,

ln (632000/742000) = ln (e^2k)
ln (632000/742000) = 2k, solve for k... (-.0802)

then to find at 2014, t=4... do 742000*e^-.0802*4= 2739261.409

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