# Graphing a exponential problem

• crm08
In summary, the problem asks to graph tangent lines to the given function y = (ln(x)/x) at the points (1,0) and (e, 1/e). The solution involves taking the derivative and finding the slope, and at the point (e,1/e) the equation of the tangent line is y = 1/e. However, there may be difficulties using a ti-89 calculator, but alternatives such as e^1 and 1/e can be used instead.
crm08

## Homework Statement

The problem asks to graph tangent lines to the given function y = (ln(x)/x, and gives the points (1,0) and (e, 1/e)

## The Attempt at a Solution

I got the answer by taking the derivative and finding the slope, and at the point (e,1/e) the equation of the tangent line is y = 1/e, but it also asks to graph the problem and using a ti-89, the only exponential button is e^(x), which requires a "x" value. Any suggestions on how to enter this tangent line on my calculator, I tried y = 1/((1+x)^(1/x)) because the denominator is the definition of "e", but it showed up as a bunch of random lines

Can you not just use $e^1$ and $\frac{1}{e^1}\equiv{e^{-1}}$ which is e and 1/e?

Last edited:

## What is an exponential function?

An exponential function is a mathematical equation that involves a constant base raised to a variable exponent. It can be written in the form f(x) = ab^x, where a is the initial value and b is the growth factor.

## What is the purpose of graphing an exponential function?

Graphing an exponential function allows us to visualize the relationship between the variable x and its corresponding output value f(x). It also helps us understand the behavior of the function, such as whether it is increasing or decreasing, and at what rate.

## How do you graph an exponential function?

To graph an exponential function, we first choose a set of input values for x and use the equation f(x) = ab^x to find the corresponding output values. These points can then be plotted on a graph and connected to create a smooth curve. It is also helpful to include the initial value and growth factor as points on the graph.

## What are the key features of an exponential graph?

The key features of an exponential graph include an initial value, a growth or decay factor, and an asymptote. The initial value is the y-intercept of the graph, the growth or decay factor determines how quickly the graph increases or decreases, and the asymptote is a line that the graph gets closer and closer to but never touches.

## How can we use graphing to solve exponential problems?

Graphing exponential functions can help us solve problems by allowing us to estimate values that are not explicitly given in the equation. We can also use the graph to identify patterns and make predictions about future values. Additionally, we can use the graph to check our answers when solving exponential equations algebraically.

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