SOLUTION: When the meteor hit the earth, there were 600,000 dinosaurs alive. Thirty years later there were only 15,000. If they died exponentially, after how many years would there be only f

Question 1091248: When the meteor hit the earth, there were 600,000 dinosaurs alive. Thirty years later there were only 15,000. If they died exponentially, after how many years would there be only five dinosaurs left?
---I believe the exponential growth/decay formula I learned is y=k⋅a^t, in this case I think it would be y=600,000(1-15,000)^30
y = amount after increase/decrease (in this case decrease)
k = original amount
a = decrease/decay factor. In this case I think it would be (1-15,000)
t = time

Answer by Boreal(15235) (Show Source): You can put this solution on YOUR website!
600000*b^t, where t=30=15000
b^30=15000/600000=1/40
30 ln b=ln (1/40)=-3.689
divide by 30 without rounding
ln b=-0.1230.
raise both sides to the e power
b=0.8843
600000*0.8843^t=5
divide by 600000
0.8843^x=5/600000=0.000008333
logs of both sides
x log (0.8843)=-5.079
x=-5.079/log (0.8843)=95.12 years ANSWER
check
in 30 years, it decreases 1/40
in 60 years, 1/1600
in 90 years, 1/64000
so it will decrease somewhat more than 1/64000
600000*(0.8843)^95=5.07
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