Identify the initial value in each formula below, and state whether the formula models exponential growth or
exponential decay. justify your responses.
b. f(t) = 2 (5 /3) ^t

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

from the law of indices we know that any number with the power 0 is equal to 1 (except 0 with the power 0)

hence the above equation becomes

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

is

> 1  or < 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 > 1 then this is an exponential growth

there is no grid

step-by-step explanation:

irrational, then, just means all the numbers that aren't rational. every integer is a rational number, since each integer n can be written in the form n/1. however, numbers like 1/2, 45454737/2424242, and -3/7 are also rational, since they are fractions whose numerator and denominator are integers.

step-by-step explanation: