Question

Jack plants a magic beanstalk that is 5 feet tall. The height of the magic beanstalk increases exponentially, doubling each day. Write a function (f) that determines the height of the beanstalk (in feet) in terms of the number of days (t) since the beanstalk was planted.

Answer 1

The function that describes the height of the magic beanstalk, which starts at 5 feet tall and doubles each day, is f(t) = 5 × 2^t.

Step-by-step explanation:

To write a function (f) that determines the height of a magic beanstalk in terms of the number of days since it was planted, given that it starts at 5 feet tall and doubles each day, we can use an exponential growth model. The function will have the form f(t) = a × b^t, where a is the initial height of the beanstalk, b is the growth rate (in this case, doubling corresponds to 2), and t is the number of days since the beanstalk was planted.

The function for the height of the magic beanstalk can be written as:

(t) = 5 × 2^t

On day tf, the height of the beanstalk will be 5 feet times 2 to the power of t.