SOLUTION: i need help with this problem: This is the model showing the percentage of Americans with heart disease who are "x" years old: 90/1+271e^-0.122x At w

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Question 377680: i need help with this problem: This is the model showing the percentage of Americans with heart disease who are "x" years old:
90/1+271e^-0.122x
At what age will the percentage of Americans with heart disease be 70%?
I'm thinking it works like this:
0.7 = 90/1+271e^-0.122x
ln 0.7= ln (90/1+271e^-0.122x)
NOW I AM STUCK!!!!! WHAT NOW???!!!! THX!!

Found 2 solutions by Fombitz, stanbon:
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
0.7+=+90%2F%281%2B271e%5E%28-0.122x%29%29
.
.
0.7%281%2B271e%5E%28-0.122x%29%29=90
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0.7%2B189.7e%5E%28-0.122x%29=90
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189.7e%5E%28-0.122x%29=89.3
.
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e%5E%28-0.122x%29=89.3%2F189.7
Now take the natural log of both sides.
-0.122x=ln%2889.3%2F189.7%29
.
.
highlight%28x=-%281%2F0.122%29ln%2889.3%2F189.7%29%29


Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
This is the model showing the percentage of Americans with heart disease who are "x" years old:
90/1+271e^-0.122x
At what age will the percentage of Americans with heart disease be 70%?
I'm thinking it works like this:
0.7 = 90/1+271e^-0.122x
----------------------------
Try this:
70 = 90/[1+271e^-0.122x]
----
1 + 271e^-0.122x = 90/70 = 1.2857
---
271e^-0.122x = 0.2857
---
e^-0.122x = 0.004744
---
Take the ln to get:
-0.122x = -5.3508
---
x = 43.86 yrs old
------------------------
Cheers,
Stan H.