Answer:
Intial Value: f(t) = 2 , Exponential Growth
Step-by-step explanation:
To find the initial value, all we have to do is find the value of f(t) at t = 0
In this case the given equation becomes
[tex]f(t) = 2(\frac{5}{3})^0[/tex]
from the law of indices we know that any number with the power 0 is equal to 1 (except 0 with the power 0)
[tex]a^0 = 1[/tex]
hence the above equation becomes
[tex]f(t) = 2(1)\\ f(t) = 2[/tex]
so the initial value is 2.
To find out whether this is exponential growth or exponential decay we need to see whether the base value of the power t is less than 1 or greater than 1, i.e. from
[tex](\frac{5}{3} )^t[/tex]
is
[tex]\frac{5}{3}[/tex] > 1 or [tex]\frac{5}{3}[/tex] < 1
if the value is greater, then with each increment in power, the total value will increase while if it is less than 1 then with each increment in power the total value will decrease.
Hence since [tex]\frac{5}{3}[/tex] > 1 then this is an exponential growth
