Unit 5: Exponential and Logarithmic Functions Essay Exponential FunctionExponential Functions: An exponential equation is a type of transcendent equation, or equation that can be solved for one factor in terms of another. An exponential function f with basis a is denoted by f (x) = ax, where a is greater than 0, a cannot be equal to 1, and x is any real number. The base 1 is excluded because 1 raised to any power gives 1. For example, 1 raised to the fourth power is 1×1×1×1, which is equal to 1. This is a constant function that is not exponential, so 1 does not can be the basis of an exponential equation. Otherwise, the base of a can be any number greater than 0 and other than 1, and x can be any real number. The equation for the parent function of an exponential function is as follows:-Domain: (-, )-Range: (0, )-Intercept: (0,1)-Increment-x-axis is the horizontal asymptote- Continuous- A x=1, y=a.This equation shifts from the main function according to the equation f(x) = k+a(xh) . In this equation, k shifts the parent function vertically, either up or down, depending on the value of k. The h value shifts the parent function left or right. If h is equal to 1, it goes right by 1 unit, if it is negative 1, it goes left by 1 unit. If a is negative, the parent function is reflected on the x-axis. If x is negative, the parent function is reflected on the y-axis. In many applications, the natural basis e is the most convenient basis in an exponential equation. The e value is approximately 2.718281828. The natural base and works just like any other base. It is easy to think of e as a substitution of a into f (x) = ax. Its graph looks like this:-Domain: (-, )-Interval: (0, )-Intercept: (0,1)-Increment-xa...... half of the sheet...... Association, If the sound of a plane taking off is 1,000,000,000,000 times the sound threshold, and if the sound of a hand drill is 10,000,000,000 times the sound threshold, during which sound would you wear hearing protection? Db(aircraft) = 10log[ I ÷ I0 ]= 10log[ (1,000,000,000,000)I0 ÷ I0 ]= 10log[1,000,000,000,000]= 120 DecibelDb(hand drill) = 10log[ I ÷ I0 ]= 10log[ (10,000,000,000)I0 ÷ I0 ]= 10log[10,0 00,000,000]= 100 decibelsConclusion: If I am near a plane taking off, I should wear ear protection and if I am near a powered hand drill , I don't need ear protection. This is because a plane taking off is 120 decibels, and the sound of a hand drill is 100 decibels, and 120 decibels is greater than 110 decibels, so you need protection, and 100 decibels is less than 110 decibels, so you don't You do need ear protection.