rewrite the equation in terms of base e. express the answer in terms of a natural logarithm and then round…

rewrite the equation in terms of base e. express the answer in terms of a natural logarithm and then round to three decimal places.\n\n( y = 110(4.9)^{x} )\n\nexpress the answer in terms of a natural logarithm.\n\n( y = 110 e^{(ln 4.9) x} ) (do not simplify.)\n\nsimplify the answer, rounding to three decimal places.\n\n( y = ) \n

rewrite the equation in terms of base e. express the answer in terms of a natural logarithm and then round to three decimal places.\n\n( y = 110(4.9)^{x} )\n\nexpress the answer in terms of a natural logarithm.\n\n( y = 110 e^{(ln 4.9) x} ) (do not simplify.)\n\nsimplify the answer, rounding to three decimal places.\n\n( y = ) \n

Answer

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})