Which of these sequences shows exponential growth?
a) 800, 400, 200, 100
b) 800, 1000, 1200, 1400
c) 100, 200, 400, 800, 1600
d) 100, 200, 300, 400, 500
e) 100, 150, 200, 250, 300
I'm pretty sure it isn't d) or e). But what is "exponential growth," exactly?
Thank you!
I think c it's growing periodically
You're right -- it's not d or e.
Check this site and I'll sure you'll figure out the right answer.
http://www.answers.com/topic/exponential-growth
Thank you so much! :)
To identify which sequence shows exponential growth, let's first understand what "exponential growth" means.
Exponential growth occurs when a quantity increases at an accelerating rate over time. In other words, if each subsequent term in a sequence is obtained by multiplying the previous term by a constant factor, then it represents exponential growth.
Now let's analyze each sequence:
a) 800, 400, 200, 100
This sequence is decreasing by dividing each term by 2, so it does not show exponential growth.
b) 800, 1000, 1200, 1400
This sequence is increasing by adding 200 to each term. It does not demonstrate exponential growth because the increase is not multiplying each term by a constant factor.
c) 100, 200, 400, 800, 1600
This sequence is increasing by multiplying each term by 2. It demonstrates exponential growth as each term is obtained by multiplying the previous term by the constant factor of 2.
d) 100, 200, 300, 400, 500
This sequence is increasing by adding 100 to each term. It does not demonstrate exponential growth because the increase is not multiplying each term by a constant factor.
e) 100, 150, 200, 250, 300
This sequence is increasing by adding 50 to each term. It does not demonstrate exponential growth because the increase is not multiplying each term by a constant factor.
Therefore, the sequence that shows exponential growth is c) 100, 200, 400, 800, 1600.