a Substitute h(t)=200 into the function and solve it for t.
B
b To find the asymptote of the function, you can use the table feature of your graphing calculator.
A
a About 5.9 weeks
B
b See solution.
Practice makes perfect
a We have been given a logistic function that models the height h (in centimeters) of the seedling after t weeks.
h(t)=256/1+13e^(-0.65t)
By substituting h(t)=200 into the function, we can find the time it takes the sunflower seedling to reach a height of 200 centimeters.
The sunflower seedling will reach a height of 200 centimeters after 5.9 weeks.
b To draw a graph on a calculator, we first press the Y= button and type the function in one of the rows. Having written the function, we can push GRAPH to draw it.
Now we will interpret the asymptote of the function. As we can see, the function approaches an h-value as t goes to positive infinity.
Therefore, it has a horizontal asymptote. To find it, we will use the table feature of the graphing calculator. We will push 2ND and WINDOW. Then, we will change the TblStart to 0 and △ Tbl to 5.
Now, by pushing 2ND and GRAPH, we can see the table.
The table shows that as t increases, h approaches to 256. This means that the maximum height of the sunflower will be 256 centimeters.
