Answer:
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 = 170.8
This tells us that as x approaches +179, the quantity 153·0.92x will be within 0.0001 of zero.