# Math Help - Exp Function Quick Question

1. ## Exp Function Quick Question

y=10(0.5)^(t/19.74)

My question: is this a horizontal stretch by a factor of 19.74?

y=10(0.5)^(8t)

My question: is this a horizontal compression by a factor of 1/8?

y=10(0.5)^x + 1

My question: is this a vertical translation of up 1 unit?

y=10(0.5)^(x-1)

My question: is this a horizontal translation one unit to the right?

Thank you

2. Originally Posted by skeske1234
y=10(0.5)^(t/19.74)

My question: is this a horizontal stretch by a factor of 19.74?

y=10(0.5)^(8t)

My question: is this a horizontal compression by a factor of 1/8?

y=10(0.5)^x + 1

My question: is this a vertical translation of up 1 unit?

y=10(0.5)^(x-1)

My question: is this a horizontal translation one unit to the right?

Thank you
Saying "horizontal/vertical stretch/compression" or "horizontal/vertical translation" makes no sense without saying what it is a stretch/compression or translation of. I assume you mean $y= 0.5^t$.

If t= 0, what is $0.5^t$? If t= 1, what is $0.5^t$. What is $0.5^1- 0.5^0$?

If x= 0, what is $10(0.5^{t/19.54})$? If x= 1, what is $10(0.5^{5/19.54})$? What is $10(0.5^{1/19.54}- 10(0.5^{0/19.54}$?

Now is that stretched or compressed? By how much?

3. ? I don't understand..

what do you mean?

are my answers correct or not