Khadija Wells

2021-02-03

To find:The year in which the 2006 cost of tuition, room and board fees in public colleges will be doubled using the function $f\left(x\right)=13,017{\left(1.05\right)}^{x}$ .

odgovoreh

Skilled2021-02-04Added 107 answers

Concept:

Modeling is a method of simulating the real life situations with mathematical equations. Using these models we can forecast the future behavior. We can translate the mathematical word problem into a math expression using variables.

Calculation:

The given model is$f\left(x\right)=13,017{\left(1.05\right)}^{x}$

Where x is the number of years since 2006 and y = f(x) is the cost in dollars.

From the table, the average annual cost in 2006 is $12,837.

After xyears the 2006 will be doubled

So, After xyears, the cost will be$2\times 12837=\mathrm{\$}25674$ .

Hence,$f\left(x\right)=13,017{\left(1.05\right)}^{x}=25674$

${\left(1.05\right)}^{x}=\frac{25674}{13017}$

Taking natural logarithm on each side

$\mathrm{ln}{\left(1.05\right)}^{x}=\mathrm{ln}\frac{25674}{13017}$

Using calculator,$x\left(In1.05\right)=0.679$

Divide by$\mathrm{ln}1.05,x=\frac{0.679}{\mathrm{ln}1.05}$

Using calculator, x = 13.92

Rounded off to nearest tens,$x\approx 13$

Hence, based on this model the 2006 cost will be doubled in 13 years since 2006.

That is, the year = 2006+13 = 2019

Final statement:

Hence, based on this model the 2006 cost will be doubled in 2019.

Modeling is a method of simulating the real life situations with mathematical equations. Using these models we can forecast the future behavior. We can translate the mathematical word problem into a math expression using variables.

Calculation:

The given model is

Where x is the number of years since 2006 and y = f(x) is the cost in dollars.

From the table, the average annual cost in 2006 is $12,837.

After xyears the 2006 will be doubled

So, After xyears, the cost will be

Hence,

Taking natural logarithm on each side

Using calculator,

Divide by

Using calculator, x = 13.92

Rounded off to nearest tens,

Hence, based on this model the 2006 cost will be doubled in 13 years since 2006.

That is, the year = 2006+13 = 2019

Final statement:

Hence, based on this model the 2006 cost will be doubled in 2019.

3m + 8 = 15 quadratic or not quadratic

What is ${2016}^{{2017}^{2018}}\equiv (mod77)$? Use Chinese Remainder Theorem and Euler's Theroem.

Find the sum of all the multiples of 3 in between 100 and 1000

Kendall reads 8 pages each night. DeSean reads 32 pages every 4 nights. Are Kendall and DeSean reading at the same rate?

Chase wants to earn at least $900 this month in commission. What is the minimum amount he needs to sell in order to earn $900 if he earns a 3.3% commission on everything he sells? Round to the nearest dollar.

If you know that a relationship is proportional and are given one order pair that is not (0,0,) how can you find another pair.

A construction worker drops his wrench. Its fall is modelled by the relation h = -4,9t²+342, where h is the height above the ground, in metres, and t is the time after the wrench was dropped in seconds. a) What is the vertex of this relation? b) What does the vertex tell us about the wrench's drop? c) How far has the wrench fallen after 5 seconds? d) When will the wrench hit the ground? What does this point represent on the graph (hint! convert to factored form)

Given A = {1, 2, 3, 4} and B = {x, y, z}. Let 𝑅 = {(1, 𝑥), (1, 𝑧), (3, 𝑦), (4, 𝑥), (4, 𝑧)}

(a) Determine the matrix of the relation.

(b) Draw Digraph of R

(c) Find the inverse of R.

(d) Determine the domain and range of R

a soup kitchen had 6 1/2 gallons of soup at the start of the day they had 2 1/10 gallons of soup left by the end of the day how maky gallons of soup did they use during the day

Find the measure of two complementary angles if one third of the first angle is 4 less then 1 third of the second angle

Jill is thrice as old as jack. Four years from now, Jill will only be twice as old as Jack. How old is Jill?

The population P of a city can be modeled by P = 250,000 e0.01t where t is the number of years since 1990. What was the population in 2002?

The population P of a city can be modeled by P = 250,000 e 0.01t where t is the number of years since 1990. What was the population in 2002?

The distance between the school and the park is 6 km. There are 1.6 km in 1 mile. How many miles apart are the school and the park?

Determine which integers in the set S: {−2, −3, −4, −5} will make the inequality 4

*p*− 7 ≥ 9*p*+ 8 true.