Rshiny-Use slider values to cacluate a dataset and plot the calculated values
Made some tweakings in your code; now it does what you want:
library(shiny)
library(ggplot2)

ui <- fluidPage(titlePanel(p("title", style = "color:#3474A7")),
                           sidebarLayout(
                             sidebarPanel(
                               sliderInput("Max", "Max:",
                                           min = 0, max = 1000,
                                           value = 116.8, step=0.1),
                               sliderInput("Rate", "Rate:",
                                           min = 0, max = 5,
                                           value = 0.12, step=0.01),
                               sliderInput("Inflection", "Inflection:",
                                           min = 0, max = 20,
                                           value = 11.06, step=0.01),
                               sliderInput("Area", "Area:",
                                           min = 0, max = 10000,
                                           value = 180, step=20),
                               downloadButton("download", "Download data"),
                               p("Made with", a("Shiny",
                                                href = "http://shiny.rstudio.com"), "."),
                             ),
                             mainPanel(
                               
                               # Output: Table summarizing the values entered ----
                               tableOutput("values"),
                               plotOutput("plot")
                               
                             )
                           )
)

#use the slider values to estimate growth for any given year using the equation
Growth = function(x, A, B, C, R) 
{R *(A *exp(-B * C^x))} 

#create a Table Ouptut with selected Slider values 
server <- function(input, output){ 
  
  # Reactive expression to create data frame of all input values ----
  
  sliderValues <- reactive({
    data.frame(
      Name = c("Max",
               "Inflection",
               "Rate",
               "Area"),
      Value = as.character(c(input$Max,
                             input$Inflection,
                             input$Rate,
                             input$Area)),
      stringsAsFactors = FALSE)
  })
  
  # Show the values in an HTML table ----
  output$values <- renderTable({
    sliderValues()
  })
  
  #reactive expression to let users download the data as a table 
  restC <- reactive({
  #run the code for all time with the selected parameters from the slider
  mylist<-list(c(1:50))
  mydata<-data.frame(lapply(mylist, Growth, A=input$Max, B=input$Rate, C=input$Inflection, R=input$Area),mylist)
  names(mydata)[1]<-"Pop"
  names(mydata)[2]<-"Time"
  mydata
  })
  #output$my_table<-renderDataTable({
  #restC() 
  # })
  #plot the values in a graph
  output$plot <- renderPlot({
    ggplot(restC(), aes(Time,Pop)) + geom_line()
  })
  
  output$download <- downloadHandler(
    filename = function() {
      paste("data-", Sys.Date(), ".csv", sep="")
    },
    content = function(file) {
      write.csv(restC(), file)
    }
  )
  
}

shinyApp(ui = ui, server = server)



I'm fairly new to Rshiny and looking for some help to understand how to create a plot using slider values as input. The user selected slider values are displayed as a table, and used as inputs to calculate an equation. The resulting calculated values are stored in a table (if possible I'd like to be able to download the generated values as a csv file) and used to generate a simple plot. This is what I have so far:
ui <- fluidPage(titlePanel(p("title", style = "color:#3474A7"),
 sidebarLayout(
                sidebarPanel(
                    sliderInput("Max", "Max:",
                                min = 0, max = 1000,
                                value = 116.8, step=0.1),
                    sliderInput("Rate", "Rate:",
                                min = 0, max = 5,
                                value = 0.12, step=0.01),
                    sliderInput("Inflection", "Inflection:",
                                min = 0, max = 20,
                                value = 11.06, step=0.01),
                    sliderInput("Area", "Area:",
                                min = 0, max = 10000,
                                value = 180, step=20),
                         p("Made with", a("Shiny",
                        href = "http://shiny.rstudio.com"), "."),
                  ),
                  mainPanel(
                    
                    # Output: Table summarizing the values entered ----
                    tableOutput("values"),
                    plotOutput("plot")
                    
                  )
                )
)


#use the slider values to estimate growth for any given year using the equation
Growth = function(x, A, B, C, R) 
{R *(A *exp(-B * C^x))} 


#create a Table Ouptut with selected Slider values 
server <- function(input, output){ 
  
  # Reactive expression to create data frame of all input values ----
  
  sliderValues <- reactive({
    data.frame(
      Name = c("Max",
               "Inflection",
               "Rate",
               "Area"),
      Value = as.character(c(input$Max,
                             input$Inflection,
                             input$Rate,
                             input$Area)),
      stringsAsFactors = FALSE)
  })
  
# Show the values in an HTML table ----
  output$values <- renderTable({
    sliderValues()
  })
    
#reactive expression to let users download the data as a table 
##restC <- reactive({
  #run the code for all time with the selected parameters from the slider
  mylist<-list(c(1:50))
  mydata<-data.frame(lapply(mylist, Growth, A=values$Max, B=values$Rate, C=values$Inflection, R=values$Area),mylist)
  names(mydata)[1]<-"Pop"
  names(mydata)[2]<-"Time"
  
 #output$my_table<-renderDataTable({
   #restC() 
# })
#plot the values in a graph
 output$plot <- renderPlot({
  ggplot(mydata, aes(Time,Pop)) + geom_line()
})

 }

shinyApp(ui = ui, server = server)

