Respuesta :
5(0.85)t < 1.5 is 15% decay
50(1.05)t < 100 is 5% growth
150(1.50)t > 500 is 50% growth
50(1.15)t < 150 is 15% growth
Answer:
1) [tex]5(0.85)^t < 1.5[/tex] has 15% decay rate.
2) [tex]50(1.05)^t < 100[/tex] has 5% growth rate.
3) [tex]150(0.50)^t > 15[/tex] has 50% decay rate.
4) [tex]15(1.50)^t > 500[/tex] has 50% growth rate.
5) [tex]50(1.15)^t > 150[/tex] has 15% growth rate.
Step-by-step explanation:
Given : Exponential inequality
To find : Match each exponential inequality to its percent rate of change.
Solution :
The exponential function is defined as [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.
If r is +ve then it is growth rate
If r is -ve then it is decay rate
1) [tex]5(0.85)^t < 1.5[/tex]
Where, a=5
1+r=0.85
r=-0.15
r=-15%
Therefore, [tex]5(0.85)^t < 1.5[/tex] has 15% decay rate.
2) [tex]50(1.05)^t < 100[/tex]
Where, a=50
1+r=1.05
r=0.05
r=5%
Therefore, [tex]50(1.05)^t < 100[/tex] has 5% growth rate.
3) [tex]150(0.50)^t > 15[/tex]
Where, a=150
1+r=0.50
r=-0.5
r=-50%
Therefore, [tex]150(0.50)^t > 15[/tex] has 50% decay rate.
4) [tex]15(1.50)^t > 500[/tex]
Where, a=15
1+r=1.50
r=0.5
r=50%
Therefore, [tex]15(1.50)^t > 500[/tex] has 50% growth rate.
5) [tex]50(1.15)^t > 150[/tex]
Where, a=50
1+r=1.15
r=0.15
r=15%
Therefore, [tex]50(1.15)^t > 150[/tex] has 15% growth rate.
