Question

Which equations represent exponential growth? Which equations represent exponential decay? Drag the choices into the boxes to complete the table.

Answer 1

Answer:

Exponential growth functions are:

$A=20000(1.08)^{t}$

$A=40(3)^{t}$

$A=1700(1.07)^{t}$

Exponential decay functions are:

$A=80(\frac{1}{2})^{t}=80(0.5)^{t}$

$A=1600(0.8)^{t}$

$A=1700(0.93)^{t}$

Step-by-step explanation:

Given:

An exponential function is of the form $y=ab^{x}$, where, $a\ne 0$.

Now, if a > 0 and b > 1, then the exponential function represent exponential growth.

If a > 0 and 0 < b < 1, then the exponential function represent exponential  decay.

Let us check each function now.

Option 1: $A=20000(1.08)^{t}$

Here, $a = 20000, b = 1.08$

As 1.08 > 1, the function is exponential growth.

Option 2: $A=80(\frac{1}{2})^{t}=80(0.5)^{t}$

Here, $a = 80, b = 0.50$

As 0.5 < 1, the function is exponential decay.

Option 3: $A=1600(0.8)^{t}$

Here, $a = 1600, b = 0.8$

As 0.8 < 1, the function is exponential decay.

Option 4: $A=40(3)^{t}$

Here, $a = 40, b = 3$

As 3 > 1, the function is exponential growth.

Option 5: $A=1700(1.07)^{t}$

Here, $a = 1700, b = 1.07$

As 1.07 > 1, the function is exponential growth.

Option 6: $A=1700(0.93)^{t}$

Here, $a = 1700, b = 0.93$

As 0.93 < 1, the function is exponential decay.