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.

Part a)

Part b)

Part c)  

Step-by-step explanation:

Part 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

we know that

100%+150%=250%=250/100=2.5

In this problem we have an exponential function of the form

where

a is the initial value

b is the base

y ----> is the rice weevil  population

x ----> the number of weeks

In this problem

a=400 rice weevils

b=2.5

substitute

Part b) Use the formula to predict the rice weevil population 10 weeks after the beginning of the study. Show your work

we have

so

For x=10 weeks

substitute

Part c) Use the formula to predict when the rice weevil population will reach 1,000,000,000.

we have

so

For y=1,000,000,000 rice weevil  population

substitute in the formula and solve for x

Simplify

Apply log both sides

what is the information provided?

step-by-step explanation: