Question

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

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

Answer:

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.

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 $y=a(1+r)^x$,

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.