**Log**

**= Log - Log**

**Log = b Log****The exponential function can be described as,y = a e^(b x)where a và b are constants. The curve that we use to lớn fit data sets is in this size so it is important lớn understand what happens when a and b are changed.Recall that any number or variable when raised to lớn the 0 power is 1. In this case if b or x is 0 then, e^0 = 1. So at the y-intercept or x = 0, the function becomes y = a * 1 or y = a. Therefore, the constant a is the y-intercept of the curve.The other parameter in our equation is b. If b is very small & greater than 0, the function flattens out. The curve increases at a slower rate then for large b"s. On the contrary, for large b"s the curve increases quickly. Look at these two plots. The first is for an equation with a large b, and the second is for a small b. Notice the scales of the plots.**

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For, b"s less than 0, the same occurs except the plots look lượt thích the plot of e^-x from above.Exercises1.)Simplify the following expressions.a.)e^(ln 2 + ln x) = 2xb.)ln(e^(1/x)) = 1/x2.)Solve for y.a.)e^(2y) = x^2 = ln(x)b.)ln(y - 1) = x + ln x = xex + 13.)Sketch the following curves on the same axes. Identify the domains of each equation in terms of x.a.)y = ln(-x) và y = -ln(x).

Domain of y = ln(-x): negative infinity to lớn zero (-inf domain of y = -ln(x): zero lớn positive infinity (0 b.)y = e^(-x) and y = -e^(x).

Domain of y = e-x: negative infinity to positive infinity (-inf tên miền of y = -ex: negative infinity lớn positive infinity (-inf Application of Exponentials4.)If you invest A dollars at a fixed annual interest rate, r and interest is compounded continuously to your account, the amount of money, Ao, you will have at the over of t years is,Ao = A e^(rt)Compounded continuously means that the money in your account is continuously being added interest.

Xem thêm: Soạn Văn 7 Cuoc Chia Tay Cua Nhung Con Bup Be, Soạn Bài Cuộc Chia Tay Của Những Con Búp Bê

It can almost be said that the interest is being added every second, day or night.a.)You deposit $621 in an trương mục that pays 10% interest. How much money will you have after 8 years? after 10 years?8 years: 621e0.8 = $1382.06110 years: 621e = $1688.053b.)How long will it take you to lớn double your money if you invest $500 at an interest rate 6%? = (0.06)/ln(2) = 11.552 yearsView answersReturn to title pageGo khổng lồ next section

Bạn đang xem: Natural log

For, b"s less than 0, the same occurs except the plots look lượt thích the plot of e^-x from above.Exercises1.)Simplify the following expressions.a.)e^(ln 2 + ln x) = 2xb.)ln(e^(1/x)) = 1/x2.)Solve for y.a.)e^(2y) = x^2 = ln(x)b.)ln(y - 1) = x + ln x = xex + 13.)Sketch the following curves on the same axes. Identify the domains of each equation in terms of x.a.)y = ln(-x) và y = -ln(x).

Domain of y = ln(-x): negative infinity to lớn zero (-inf domain of y = -ln(x): zero lớn positive infinity (0 b.)y = e^(-x) and y = -e^(x).

Domain of y = e-x: negative infinity to positive infinity (-inf tên miền of y = -ex: negative infinity lớn positive infinity (-inf Application of Exponentials4.)If you invest A dollars at a fixed annual interest rate, r and interest is compounded continuously to your account, the amount of money, Ao, you will have at the over of t years is,Ao = A e^(rt)Compounded continuously means that the money in your account is continuously being added interest.

Xem thêm: Soạn Văn 7 Cuoc Chia Tay Cua Nhung Con Bup Be, Soạn Bài Cuộc Chia Tay Của Những Con Búp Bê

It can almost be said that the interest is being added every second, day or night.a.)You deposit $621 in an trương mục that pays 10% interest. How much money will you have after 8 years? after 10 years?8 years: 621e0.8 = $1382.06110 years: 621e = $1688.053b.)How long will it take you to lớn double your money if you invest $500 at an interest rate 6%? = (0.06)/ln(2) = 11.552 yearsView answersReturn to title pageGo khổng lồ next section