Give a possible formula for the exponential function in the figure below.
round any calculations to two decimal places.
y =

The exponential function is

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 , 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

∴

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

∴

- Divide both sides by 400

∴

- Take ∛ for both sides

∴ ∛80 = b

∴ b = 4.31

∴

* The exponential function is

hope this !

step-by-step explanation:

d = distance between moon and sun, which in this problem is the hypotenuse of a right triangle.  

the distance y is the side opposite to angle x in the right triangle.   use the definition of the sine function from basic trigonometry.

sin(x) = y/d ⇒

d = y/sin(x)

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step-by-step explanation: