Question

PLSSSS HELP 20 POINTS ! Match each exponential inequality to its percent rate of change.

85% decay
85% growth
50% decay
5% growth
15% decay
50% growth
15% growth
5% decay

5(0.85)t < 1.5
50(1.05)t < 100
150(0.50)t > 15
15(1.50)t > 500
50(1.15)t < 150

Answer 1

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 2

1)
`5(0.85)^t < 1.5` has 15% decay rate.

2)
`50(1.05)^t < 100` has 5% growth rate.

3)
`150(0.50)^t > 15` has 50% decay rate.

4)
`15(1.50)^t > 500` has 50% growth rate.

5)
`50(1.15)^t > 150` has 15% growth rate.

Explanation:

Given : Exponential inequality

To find : Match each exponential inequality to its percent rate of change.

Solution :

The exponential function is defined as
`y=a(1+r)^x`,

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)
`5(0.85)^t < 1.5`

Where, a=5

1+r=0.85

r=-0.15

r=-15%

Therefore,
`5(0.85)^t < 1.5` has 15% decay rate.

2)
`50(1.05)^t < 100`

Where, a=50

1+r=1.05

r=0.05

r=5%

Therefore,
`50(1.05)^t < 100` has 5% growth rate.

3)
`150(0.50)^t > 15`

Where, a=150

1+r=0.50

r=-0.5

r=-50%

Therefore,
`150(0.50)^t > 15` has 50% decay rate.

4)
`15(1.50)^t > 500`

Where, a=15

1+r=1.50

r=0.5

r=50%

Therefore,
`15(1.50)^t > 500` has 50% growth rate.

5)
`50(1.15)^t > 150`

Where, a=50

1+r=1.15

r=0.15

r=15%

Therefore,
`50(1.15)^t > 150` has 15% growth rate.