research indicates that in a controlled environment the number of diseased mice will increase linearly at the rate of 3 mice per day after one of the mice in the cage is infected with a particular type of disease-causing germ A) write An equation That Will give the number of diseased mice after any given number of days. B) if there were 40 mice in the cage, how long will it take until they are all infected?
A) y = 1+3x
B) 1+3x = 40, so 13 days
A) Let's denote the number of days as 'd' and the number of diseased mice as 'n'. We know that after one mouse is infected, the number of diseased mice will increase linearly at a rate of 3 mice per day.
Therefore, the equation would be:
n = 3d
B) If there are 40 mice in the cage and we want to find out how long it will take until they are all infected, we can set up the equation:
40 = 3d
To find the value of 'd', we need to isolate it on one side of the equation. We can do this by dividing both sides by 3:
40/3 = d
Now, let's calculate the value of 'd':
d ≈ 13.333
Therefore, it will take approximately 13.333 days for all 40 mice in the cage to become infected.
A) To write an equation that gives the number of diseased mice after any given number of days, we need to define some variables. Let's use "t" to represent the number of days and "D" to represent the number of diseased mice.
Since the research indicates that the number of diseased mice increases linearly at a rate of 3 mice per day after one mouse is infected, we can write the equation as:
D = 3t + 1
In this equation, we add 1 because initially, there is one diseased mouse. So after each day, the number of diseased mice increases by 3.
B) If there were 40 mice in the cage, we can use the equation we derived in part A and solve for "t" when D = 40. Substituting D = 40 into the equation:
40 = 3t + 1
Now, let's solve for "t":
3t = 40 - 1
3t = 39
Divide both sides of the equation by 3:
t = 39 / 3
t = 13
Therefore, it will take 13 days until all 40 mice in the cage are infected with the disease.