Answer:
She gained 24,000 votes between the second and fifth day.
She has 32,000 votes on day 5.
Step-by-step explanation:
The rate at which the candidate gains votes as a function of time, in days, is given by:
[tex]f(t)=2000t+1000[/tex]
Integrating this function yields the accumulated total number of votes gained at each day:
[tex]\int {f(t)} \, dt=\int {(2000t+1000)} \, dt \\F(t)=1000t^2 +1000t +c[/tex]
a. Applying the given interval between days two and five, the total number of votes gained is:
[tex]F(5)-F(2)=(1000*5^2 +1000*5+c)-(1000*2^2 +1000*2+c)\\F(5) - F(2) = 24,000[/tex]
There was a change of 24,000 votes gained between the second and fifth day.
b. Assuming that she started of with 2000 votes, the total number of votes on day 5 is:
[tex]V= 2000 +F(5)-F(0)\\V=2000+(1000*5^2 +1000*5+c)-(1000*0^2 +1000*0+c)\\V=32,000[/tex]
She has 32,000 votes on day 5.
