Question

Does each equation represent exponential decay or exponential growth?

Answer 1

Answer:

1. $H = 5.9(0.82)^{t}$. Exponential decay function.

2. $y = 0.8(3.6)^{t}$. Exponential growth function.

3. $f(t) = 0.72(15)^{t}$. Exponential growth function.

4. $A = \frac{4}{9} (8)^{t}$. Exponential growth function.

5. $A = (\frac{4}{3})^{t}$. Exponential growth function.

6.  $H = \frac{7}{2} (\frac{5}{6} )^{t}$. Exponential decay function.

7. g(x) = 0.3(x). Not an exponential function.

Step-by-step explanation:

1. $H = 5.9(0.82)^{t}$. This is an exponential decay function.

As the value of t increases H-value decreases.

2. $y = 0.8(3.6)^{t}$. This is an exponential function of growth.

As the value of t increases y-value also increases.

3. $f(t) = 0.72(15)^{t}$. This is an another example of exponential growth function.

As the value of t increases f(t)-value also increases.

4. $A = \frac{4}{9} (8)^{t}$. This is again an example of exponential growth function.

As the value of t increases A-value also increases.

5. $A = (\frac{4}{3})^{t}$. This is again an example of exponential growth function.

As the value of t increases A-value also increases.

6. $H = \frac{7}{2} (\frac{5}{6} )^{t}$. This is another an example of exponential decay function.

As the value of t increases, H-value decreases.

7. g(x) = 0.3(x). This is a non-exponential function. (Answer)