Answer:
Y(n) = 400(2.5)^n
Y = 3,814,697 rice weevils
16.1 weeks
Step-by-step explanation:
To predict the population of rice weevil for any week after the start of the study ; wwe use an exponential function for this purpose :
y(n) = A(1 + r)^n
Where;
Y(n) = population at week n
r = growth rate ; n = number of weeks
A = initial population at the start of the study
r = 150% = 1.5
Hence, we have the equation :
Y(n) = 400(1 + 1.5)^n
Y(n) = 400(2.5)^n
B.)
Population after 10 weeks
n = 10
Y(10) = 400(2.5)^10
Y = 400 * 9536.7431640625
Y = 3814697.265625
Y = 3,814,697 rice weevils
C)
When population will reach 1,000,000,000
We have :
1,000,000,000 = 400(2.5)^n
1000000000 / 400 = 2.5^n
2500000 = 2.5^n
Take the log of both sides :
log(2500000) = nlog(2.5)
6.3979400 = n * 0.3979400
n = 6.3979400 / 0.3979400
n = 16.077649
n = 16.1 weeks approximately
