(0.9)^t-4 rewrite the function to determine if its exponential growth or decay.

Question

I get the part where its 0.9^t over 0.9^4, then it would be 0.9^t over 0.7, but then the answer in the book is 1.52(0.9)^t. I would like to know where the 1.52 came from.

Answer 1

Hello Jeffy,

Based on the answer you say the book gave, here is how you want to type the original problem:

y = .9^(t-4).

 

Instead of using .7, use the actual value for .9^4 = .6561.  Then, since it is in the denominator, you want:

1 / .6561, which gives you approximately 1.52.

 

Alternatively, approach it as follows:

 

Using properties of exponents, you can re-write as:

y = (.9^t) * (.9^(-4))  {Working in reverse, I am using that when multiplying like bases, you add the exponents}

 

If you throw .9^(-4) in the calculator, you get approximately 1.52.

 

So the equation becomes:

y  = (.9^t) * (1.52)

→ y = 1.52(.9^t)

 

Hope the above helps, and thank you for posting the question.

Michael Ehlers