Question

Determine which of the following exponential formula(s) represents II and IV in the graph above.

Answer 1

Answer:

A $\alpha ,\beta$

Step-by-step explanation:

Step 1

The first step is to notice that the graphs of II and iv have the same y intercept. This means that we are looking for functions that match the condition that when t=0, the two functions have the same value.  The functions $10(1.02)^t,10(1.05)^t$ meet that condition. Additionally the functions  $30(0.95)^t,30(1.05)^t$ meet this condition.

Step 2

The other condition that must be met by the 2 functions is that they should both increase with the increase in increasing values of t.  the function  $30(0.95)^t$ does not meet this condition. This means that only the functions $\alpha ,\beta$ are the only functions that meet this condition.

Answer 2

Answer:

a. α and β

Step-by-step explanation:

One way to solve this exercise is by analyzing the y - intercept of the functions.

By looking at the graph, we can see that II and IV have the same y - intercept.

All the formulas below depend of the variable ''$t$'' so if we want to find the y - intercept we only need to replace by ''$t=0$'' in the formulas.

We can also see that the y - intercept of II and IV will be the lower that the another y - intercept of the functions.  

If we replace by $t=0$ :

(α)(t) = $10.(1.02)^{t}$ ⇒ $10.(1.02)^{0}=10$

(β)(t) = $10.(1.05)^{t}$ ⇒ $10.(1.05)^{0}=10$

(χ)(t) = $20.(1.02)^{t}$ ⇒ $20.(1.02)^{0}=20$

(δ)(t) = $30.(0.85)^{t}$ ⇒ $30.(0.85)^{0}=30$

(ε)(t) = $30.(0.95)^{t}$ ⇒ $30.(0.95)^{0}=30$

(Φ)(t) = $30.(1.05)^{t}$ ⇒ $30.(1.05)^{0}=30$

We find that the lowest y - intercept (also equal) are the y - intercept of α and β. Therefore, the correct option is a. α and β