Question

Identify the initial value in each formula below, and state whether the formula models exponential growth or

exponential decay. Justify your responses.
c. f(t) = 2 / 3 (3)t

Answer 1

Answer: Hello mate!

the equation is written is:

f(t) = 2 / 3 (3)t

And is hard to work with this, but let's try:

I will interpret this function in two ways:

f(t) = (2/3^(3t)) in this case, the exponential part is in the denominator, so when t increases, the denominator also increases, if the denominator increases, the value of the function decreases, then, in this case, we have an exponential decay.

second case:

f(t) = (2/3)^(3t) the case is similar.

we know that 2/3 < 1

now, (2/3)^3t = (2^3t/3^3t)

3 is a number bigger than 2, then 3^3t > 2^3t, meaning that when t increases, bot denominator, and numerator increases, but the denominator increases faster, this means that we still have an exponential decay.