Which equations represent exponential growth?
Which equations represent exponential decay?
Drag the choices into the boxes to complete the table.
Exponential Growth: y=4000(1.0825)^t ,y=12,000(0.72)^t , y=8000(0.97)^t ,
Exponential Decay: y=1700(1.25)^t , y=240(1/2)^t , y=1.5(10)^t
You did not show your answers, how can we check ?
.99999....^t ---> smaller and smaller
1.000001^t ---> bigger and bigger
try it on your calculator :)
i am not correct
you are correct that
b^x
is growth if b>1 and decay if b<1
To determine whether an equation represents exponential growth or decay, we need to examine the base of the exponential term. If the base is greater than 1, it represents exponential growth. On the other hand, if the base is between 0 and 1, it represents exponential decay.
Let's go through each equation one by one:
Exponential Growth:
1. y = 4000(1.0825)^t: The base of the exponential term is 1.0825, which is greater than 1. Therefore, this equation represents exponential growth.
2. y = 12,000(0.72)^t: The base of the exponential term is 0.72, which is between 0 and 1. Therefore, this equation represents exponential decay.
3. y = 8000(0.97)^t: Similar to the previous equation, the base 0.97 is between 0 and 1. Hence, this equation represents exponential decay.
Exponential Decay:
1. y = 1700(1.25)^t: The base of the exponential term is 1.25, which is greater than 1. Thus, this equation represents exponential growth.
2. y = 240(1/2)^t: The base of the exponential term is 1/2, which is between 0 and 1. Hence, this equation represents exponential decay.
3. y = 1.5(10)^t: The base of the exponential term is 10, which is greater than 1. Therefore, this equation represents exponential growth.
Now, let's put these equations in the correct boxes:
Exponential Growth:
- y = 4000(1.0825)^t
- y = 1.5(10)^t
Exponential Decay:
- y = 12,000(0.72)^t
- y = 8000(0.97)^t
- y = 240(1/2)^t
I hope this clarifies which equations represent exponential growth and decay!