Question

Drag the tiles to the correct boxes to complete the pairs. not all tiles will be used.

Match each exponential inequality to its percent rate of change.

Answer 1

50% growth; 15% decay; 50% decay; 15% growth; 5% growth.

Explanation:

These equations are of the form

`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.

In the first equation,

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

`5(0.85)^t<1.5`, 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,

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

`50(1.15)^t<150`, 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,

`50(1.05)^t<100`, 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.