Question

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 = 110(4.9)^{x} )

express the answer in terms of a natural logarithm.

( y = 110 e^{(ln 4.9) x} ) (do not simplify.)

simplify the answer, rounding to three decimal places.

( y = )

Explanation:

Step1: Use the property \(a^x = e^{x\ln a}\)

We know that for any positive number \(a\), \(a^x=e^{x\ln a}\). Here \(a = 4.9\), so \(y = 110(4.9)^x\) can be rewritten as \(y=110e^{(\ln 4.9)x}\).

Step2: Calculate \(\ln 4.9\)

Using a calculator, \(\ln 4.9\approx1.589\).

Answer:

\(y = 110e^{1.589x}\)