Question

Graded Assignment Unit Test, Part 2: More Math Models Answer the questions. When you have finished, submit this assignment to your teacher by the due date for full credit. Total score: ____ of 18 points (Score for Question 1: ___ of 10 points) 1. There are 400 rice weevils at the beginning of an insect study. The population is expected to grow at a rate of 150% each week. (a) Write and simplify a formula that can be used to predict the rice weevil population for any week after the beginning of the study. (b) Use the formula to predict the rice weevil population 10 weeks after the beginning of the study. Show your work. (c) Use the formula to predict when the rice weevil population will reach 1,000,000,000. Show your work. Answer:

Answer 1

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