SOLUTION: The amount of a chemical that will dissolve in a solution increases exponentially as the (Celsius) temperature t is increased according to the model A(t) = 10e^0095t At what temp

Algebra ->  Logarithm Solvers, Trainers and Word Problems -> SOLUTION: The amount of a chemical that will dissolve in a solution increases exponentially as the (Celsius) temperature t is increased according to the model A(t) = 10e^0095t At what temp      Log On


   



Question 758711: The amount of a chemical that will dissolve in a solution increases exponentially as the (Celsius) temperature t is increased according to the model
A(t) = 10e^0095t
At what temperature will 15 g dissolve ?

Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
+A%28t%29+=+10%2Ae%5E%28.0095t%29+
given:
+A%28t%29=+15+
+15+=+10%2Ae%5E%28.0095t%29+
Take the natural log of both sides
+ln%28+15+%29+=+ln%28+10+%29+%2B+ln%28+e%5E%28+.0095t+%29+%29+
+ln%28+15+%29+=+ln%28+10+%2B+.0095t+%29+
+.0095t+=+ln%2815%29+-+ln%2810%29+
+.0095t+-+ln%28+15%2F10+%29+
+.0095t+=+ln%28+1.5+%29+
+t+=+ln%28+1.5+%29+%2F+.0095+
+t+=+.4055+%2F+.0095+
+t+=+42.681+ degrees Celsius
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check:
+15+=+10%2Ae%5E%28.0095%2A42.681%29+
+15+=+10%2Ae%5E.4055+
+15+=+10%2A1.5001+
+15+=+15.001+
close enough