Answer:
[tex]y=3^x[/tex]
Step-by-step explanation:
Exponential Growth Function
The exponential function is often used to model natural growing or decaying processes, where the change is proportional to the actual quantity.
An exponential growth function is expressed as:
[tex]C(t)=C_o\cdot(1+r)^t[/tex]
Where:
C(t) is the actual value of the function at time t
Co is the initial value of C at t=0
r is the (positive) growth rate, expressed in decimal
Since r is positive, 1+r is greater than 1.
From the available options, only the last two of them correspond to exponential functions according to the definition above.
Note the third option has a base of 1/3 which is not greater than 1. In fact, it corresponds to an exponential decay function.
The last option has a base 3 and corresponds to a value of r=2 which correctly fits with the definition presented above, thus the correct choice is
[tex]\mathbf{y=3^x}[/tex]
