Answer:
50% growth; 15% decay; 50% decay; 15% growth; 5% growth.
Step-by-step explanation:
These equations are of the form
[tex]y=a(1+r)^x[/tex], where a is the original amount, r is the amount of growth or decay, and x is the number of time periods.
In the first equation,
[tex]15(1.50)^t>500[/tex], the value of a is 15. The value of 1+r is 1.50.
We can use an equation to find r, the amount of growth:
1+r = 1.50
Subtract 1 from each side:
1+r-1 = 1.50-1
r = 0.50
This means the rate is 0.50, or 50%; this is growth.
For the second equation,
[tex]5(0.85)^t<1.5[/tex], the value of 1+r is 0.85:
1+r = 0.85
Subtract 1 from each side:
1+r-1 = 0.85-1
r = -0.15
This means the rate is -0.15, or -15%; this is decay.
For the third equation,
[tex]150(0.50)^t>15[/tex], the value of 1+r is 0.50:
1+r = 0.50
Subtract 1 from each side:
1+r-r = 0.50-1
r = -0.50
This means the rate is -0.50, or -50%; this is decay.
For the fourth equation,
[tex]50(1.15)^t<150[/tex], the value of 1+r is 1.15:
1+r = 1.15
Subtract 1 from each side:
1+r-1 = 1.15-1
r = 0.15
This means the rate is 0.15, or 15%; this is growth.
For the last equation,
[tex]50(1.05)^t<100[/tex], the value of 1+r is 1.05:
1+r = 1.05
Subtract 1 from each side:
1+r-1 = 1.05-1
r = 0.05
This means the rate is 0.05, or 5%; this is growth.
