MATH SOLVE

4 months ago

Q:
# What value will x have to for the first number to reach zero 153•0.92^x

Accepted Solution

A:

Answer:Step-by-step explanation:153•0.92^x is a decaying exponential function.In theory these functions never reach zero.Suppose that you were willing to change the problem to read:"What value will x have to for the first number to come within 0.0001 of zero?" Solve 153•0.92^x = 0.0001.To do this, take the common log of both sides, obtaining log 153 + x*log 0.92 = log 0.0001 Note that log 0.0001 = -4; log 153 = 2.18469; and log 0.92 = -0.03621.Then we have:2.18469 + x(-0.03621) = - 4.Isolate the 2nd term. To accomplish this, subtract 2.18469 from both sides, obtaining:-0.03621x = -6.18469 Isolate x by dividing both sides by -0.03621:x = 170.8This tells us that as x approaches +179, the quantity 153·0.92x will be within 0.0001 of zero.