Question

name colin k date 2/12/26 pd 2a
algebra 2
unit 5 quiz 1 (v1)

1. selected response - 1 point

jalen shared a new tiktok online. the number of views it had for the first 4 days are shown in the table here. let t represent the time in days and v(t) represent the number of views.
which of the following explicit formulas best models the situation?
a. $v(t)=3.5t + 50$
b. $v(t)=50 + 3.5(t - 1)$
c. $v(t)=50(3.5)^{t-1}$
d. $v(t)=50(0.29)^{t}$

Explanation:

Step1: Check linear vs exponential growth

Calculate the ratio of consecutive views:
$\frac{175}{50}=3.5$, $\frac{612.5}{175}=3.5$, $\frac{2143.75}{612.5}=3.5$
Growth is exponential, not linear (eliminates a, b).

Step2: Test exponential formulas

For $t=1$, check option c: $v(1)=50(3.5)^{1-1}=50(1)=50$ (matches table).
Check option d: $v(1)=50(0.29)^{1}=14.5$ (does not match).

Step3: Verify with t=2

Option c: $v(2)=50(3.5)^{2-1}=50(3.5)=175$ (matches table).

Answer:

c. $v(t) = 50(3.5)^{t-1}$