SOLUTION: Rewrite the equation in terms of base e. Express the answer in terms of a natural logarithm and then round to three decimal places. y=101(4.8)x Part 1 Express the answer in te

Algebra ->  Test -> SOLUTION: Rewrite the equation in terms of base e. Express the answer in terms of a natural logarithm and then round to three decimal places. y=101(4.8)x Part 1 Express the answer in te      Log On


   

Question 1197628: Rewrite the equation in terms of base e. Express the answer in terms of a natural logarithm and then round to three decimal places.
y=101(4.8)x
Part 1
Express the answer in terms of a natural logarithm.
y=_________
Part 2:
Simplify the​ answer, rounding to three decimal places.
y=________
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!



Part 1
Express the answer in terms of a natural logarithm.
Exponential expressions with natural base e are of the form y+=+a%2Ae%5E%28kx%29. The value of 'a' is already set to be 3.4 since this is the coefficient of the given equation. We just need to find k


So set %280.4%29%5Ex equal to e%5E%28kx%29 and solve for k
%284.8%29%5Ex+=+e%5E%28kx%29
%284.8%29%5Ex+=+%28e%5Ek%29%5Ex
4.8+=+e%5Ek The two sides have the same exponent of x. So the two bases are 4.8 and e%5Ek must be equal.
ln%284.8%29+=+k Convert to logarithmic form
k+=+ln%284.8%29

y+=+101%2Ae%5E%28ln%284.8%29x%29


Part 2:
Simplify the​ answer, rounding to three decimal places.
y+=+101%2Ae%5E%28ln%284.8%29x%29..............ln%284.8%29=1.5686159179138452=1.569
y+=+101%2Ae%5E%281.569x%29