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Write a function in terms of t that represents the situation.
Sales of $10,000 increase by 65% each year.
y =
13

Sagot :

Absor201idn

Answer:

A function in terms of t that represents the situation is:

[tex]\:y\:=\:10,000\left(1.65\right)^t[/tex]

Step-by-step explanation:

We know that the exponential growth function is of the form

[tex]y\:=\:a\:\left(1\:+\:r\right)^t[/tex]

Here:

  • a = initial value
  • r = growth rate  
  • t = number of time intervals that have passed

As the sales of $10,000 represent an initial condition. Thus,  

a = 10,000

Given that sales are increased by 65% every year.

r = 65% = 0.65

now substituting a = 10,000 and r = 0.65 in the function

[tex]y\:=\:10,000\left(1\:+\:0.65\right)^t[/tex]

[tex]\:y\:=\:10,000\left(1.65\right)^t[/tex]

Therefore, a function in terms of t that represents the situation is:

[tex]\:y\:=\:10,000\left(1.65\right)^t[/tex]

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