Question

Give a possible formula for the exponential function in the figure below.

Answer 1

Answer:

The exponential function is $y=400(4.31)^{t}$

Step-by-step explanation:

* Lets look to the graph and describe it

- The graph is an exponential function function

- It is a relation between t and y

- t is represented by x-axis

- Y is represented by y-axis

- The vale of y is 400 when t = 0

- The value of y is 32,000 when t = 3

* We have two point on the graph so we can make the equation

- The form of the exponential function is $y=a(b)^{t}$, where

  a is the initial value and b is the growth factor

∵ The graph of the function is growth exponential function

∴ b is greater than 1

∵ The points (0 , 400) and (3 , 32000) lie on the function

∵ y = 400 when t = 0

∴ the initial value is 400

∴ a = 400

∴ $y=400(b)^{t}$

- Substitute the values of y and t by the second point

∴ $32000=400(b)^{3}$

- Divide both sides by 400

∴ $80=(b)^{3}$

- Take ∛ for both sides

∴ ∛80 = b

∴ b = 4.31

∴ $y=400(4.31)^{t}$

* The exponential function is $y=400(4.31)^{t}$