Question

Rewrite the equation y=110(4.2)x in terms of base e. Express the answer in terms of a natural logarithm and then round to three decimal places.

Answer 1

To rewrite the equation y=110(4.2)x in terms of base e, we can express it as y = 110e^(ln(4.2)x). Substituting the approximate decimal value of ln(4.2), the equation becomes y ≈ 110e^(1.435x).

Step-by-step explanation:

To rewrite the equation y=110(4.2)x in terms of base e, we can use the property that ab can be expressed as e raised to the power of ln(ab). So, we rewrite the equation as:

y = 110eln(4.2)x

Now, if we substitute the value of ln(4.2) with its approximate decimal value of 1.435, we get:

y ≈ 110e1.435x

Therefore, the equation y=110(4.2)x rewritten in terms of base e is approximately y ≈ 110e1.435x.