Answer:
it will take 1 day for 1000 cattle to be infected.
Step-by-step explanation:
It seems there might be a typographical error in the function you provided. The expression "40(25)" doesn't represent a mathematical operation. However, I'll assume that you meant C(n) = 40 \cdot 25^nC(n)=40⋅25
n
, where nn is the number of days.
Given this assumption, let's proceed with the calculations:
a) To find out how many cattle had the virus initially (i.e., at n = 0n=0), we can plug in n = 0n=0 into the function C(n)C(n):
C(0) = 40 \cdot 25^0 = 40 \cdot 1 = 40C(0)=40⋅25
0
=40⋅1=40.
So, initially, there were 40 cattle infected with the virus.
b) To find out how many cattle will be affected in 1 week (7 days), we can plug in n = 7n=7 into the function C(n)C(n):
C(7) = 40 \cdot 25^7C(7)=40⋅25
7
.
You can calculate the numerical value of C(7)C(7) using a calculator:
C(7) \approx 4062500000C(7)≈4062500000.
So, approximately 4,062,500,000 cattle will be affected in 1 week.
c) To find out how long it will take until 1000 cattle are infected, we need to solve for nn in the equation C(n) = 1000C(n)=1000:
40 \cdot 25^n = 100040⋅25
n
=1000.
Divide both sides by 40:
25^n = \frac{1000}{40} = 2525
n
=
40
1000
=25.
Take the logarithm base 25 of both sides:
n = \log_{25}(25) = 1n=log
25
(25)=1.
So, it will take 1 day for 1000 cattle to be infected.
Keep in mind that my interpretation of the function might be different from what you intended, so please verify the function and the calculations accordingly.