n Exercises 92–93, rewrite the equation in terms of base e. Expre...

Question

n Exercises 92–93, 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 = 6.5(0.43)^x

Accepted Answer

Hello. Today we're going to rewrite an equation involving terms of e. So the equation given to us is why equal to 1.9 times 0.88 raised to the power of X. Now, in order to rewrite this into a form involving E. Let's go ahead and just recall that when we have an equation in the form of Y is equal to A times B raised to the power of X. This statement can be rewritten as Y is equal to eight times E raised to the power of X times Ln of B. So this is what we're going to use to rewrite this equation with terms of E. Now let's go ahead and identify what are A and B are in this case A is going to be the number in front of our exponential value right now. So it's gonna be a is going to be 1.9 And B is going to be the exponential value. So B is going to equal to 0.88. Now, what we're gonna do with these two values is plug it into an equation in this format here. So y is equal to a which is 1.9 times E race the power of X times Ln of B which is Ellen of 0.88. Now we can go ahead and evaluate what Alan of 0.88 is by plugging it into a calculator. Putting this value into a calculator is going to give us the approximate value of -0.128. So replacing this natural log of 0.88 with this decimal value is going to give us the equation, Y is equal to 1.9 times e. Race the power of negative 0. times x. And this is going to be our solution. That also means that the solution to this problem is going to be D. So I hope this video helps you in understanding this process and I'll go ahead and see you all in the next video.

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