Give an example of an exponential expression. What exponential equation is equivalent to the logarithmic equation log_a b = c? How to linearize exponential? How do you find an exponential function given two points? Suppose that f is an exponential function with f(2) = 4 and f(3) = 15...
Lesson7.5 Wehavestudiedseveralwaystosolvequadraticequations.◦Wecanfindthex-interceptsonagraph,◦Wecansolvebycompletingthesquare,or◦Wecanusethequadraticformula. Whathappensifyoutrytousethequadraticformulaonanequationwhosegraphhasnox-intercepts? Thegraphofy=x2+4x+5atrightshowsthatthisfunctionhasnox-intercepts...
What is the difference between relation and function in discrete maths? How do you use a calculator to solve an expression with exponents like B^3 / B^-6. For example, why does the calculator return an unexpected answer when inputting 5^3 x 5^6?
Since you can be sure the point (0,1) will appear in an exponential graph, use it as the anchor point for your sketch if asked to transform the graph of an exponential function. Example 1:Sketch the graph ofh(x) = −3x+ 2− 1. ...
When the unknown x appears as an exponent, then to “free” it, take the inverse function of both sides. In this example, take the logarithm with base 5 of both sides. In general, if we have any equation, f(x) = a, then if g is the inverse of f: ...
For parts b and c, it is asking you to use the function they gave you to find specific output values. For example, part b is asking you to find the population at t=0, which means that you can plug 0 into the function for t. When you do this, remember that e is a constant (...
It means the slope is the same as the function value (the y-value) for all points on the graph. Example: Let's take the example when x = 2. At this point, the y-value is e2≈ 7.39.Since the derivative of ex is ex, then the slope of the tangent line at x = 2 is also e2...
Note that the little o requirement is harder to fulfill, meaning that if a function f is little o of a function g, it is also Big O of g, and it means the function g grows faster than if it were just Big O of g. In your example, if b is 3 and a is 2 and we set k to...
By reversing the process in obtaining the derivative of the exponential function, we obtain the remarkable result:∫eudu=eu+K∫eudu=eu+KIt is remarkable because the integral is the same as the expression we started with. That is, eueu....
1. With what kind of exponential model would half-life be associated? What role does half-life play in these models? 2. What is carbon dating? Why does it work? Give an example in which carbon dating would be useful. 3. With what kind of exponential model would doubling time be ...