Answer:
[tex]y=3(1-0.451)^t[/tex]
The value of r is 0.451
The percentage decrease is about 45.1%
Step-by-step explanation:
The given exponential function is [tex]y=3e^{-0.6t}[/tex]
Using the exponent rule, [tex](x)^{ab}=(x^a)^b[/tex]
[tex]y=3(e^{-0.6})^t[/tex]
Now the value of [tex]e^{-0.6}=0.5488[/tex]
Thus, we can rewrite the function as
[tex]y=3(0.5488)^t[/tex]
Therefore, the function in form [tex]y=a(1-r)^t[/tex]
[tex]y=3(1-0.451)^t[/tex]
The value of r is 0.451
The percentage decrease is about 0.451 ×100 = 45.1%
