How to sole linear equations
2 answers:
You might be interested in
We are told that a population of insects grows exponentially and we are given a table of data about insect population growth. We are asked to find population of insects at the end of week 11.
The initial insect population is 20 and at the end of 1st week population increases to 30.
Let us find growth percentage of insect population,
We can see that insect population is growing at rate of 50% per week.
Now let us write an exponential function for our population.
, where P(w) represents population at the end of w weeks.
Let us substitute w=11 in our function to find insect population at the end of 11 weeks.
Therefore, population of insects at the end of 11th week will be 1730.
To check how much Tim will pay to refill the gas tank using one of the on-site pumps, we can create a linear model. We know from our problem that the Renter's charge $4.50 per gallon plus a $5.00 refueling, so let 
be the number of gallons and 
the total cost.
We also know that the fuel tank in the car is half empty and t<span>he car has a 12-gallon fuel tank, so half tank is 6 gallons. Lets replace the number of gallons in our linear model with 6 to fin the total cost:
</span>
Now, to find how much Tim will pay if he decides to refuel the car on his own, we can also create a linear model.
Let be the number of gallons and the total cost. We know form our problem that <span>refueling the car on his own will cost $2.59 per gallon and the late fee charge is $32.
</span>
<span>We already know that half tank is 6 gallons, so
</span>
<span>
Comparing the result of our two linear models we can conclude that the correct answer is: </span><span>b. It would be cheaper to return the car on time and pay the refueling costs.</span>
We also know that the fuel tank in the car is half empty and t<span>he car has a 12-gallon fuel tank, so half tank is 6 gallons. Lets replace the number of gallons in our linear model with 6 to fin the total cost:
</span>
Now, to find how much Tim will pay if he decides to refuel the car on his own, we can also create a linear model.
Let
</span>
<span>We already know that half tank is 6 gallons, so
</span>
<span>
Comparing the result of our two linear models we can conclude that the correct answer is: </span><span>b. It would be cheaper to return the car on time and pay the refueling costs.</span>