Word problems

[rachelmaddie]

Is this correct?

Apply the growth formula to find when the sale of cars will be more than the sale of motorcycles.
y = a (1 + r) x
where, a = initial amount, r = growth rate as a decimal, x = number of time intervals passed (days, months, years), and y = amount after x time
Equation for motorcycles: y = 5.75(1 + 0.16) x
Equation for cars: y = 3.5(1 + 0.25) x

3.5(1 + 0.25) x > 5.75(1 + 0.16) x
3.5(1.25) x > 5.75(1.16) x
3.5(1.25) x > 5.75(1.16) x
(1.25) x / (1.16) x > 5.75/3.5
(1.25 / 1.16) x > 1. 64285714286
x * In (1.25 / 1.16) x > In (1.64285714286)
x > In(1.64285714286/In(1.25/1.16)
x > 6.6436473051
In approximately 6.644 years, the sale of cars will be more than the sale of motorcycles.

 

[Dr.Peterson]

Here is what you wrote, with exponents indicated properly (using the [MATH]x^2[/MATH] button on the edit bar):

Apply the growth formula to find when the sale of cars will be more than the sale of motorcycles.​

y = a (1 + r)^x​

where, a = initial amount, r = growth rate as a decimal, x = number of time intervals passed (days, months, years), and y = amount after x time​

Equation for motorcycles: y = 5.75(1 + 0.16)^x​

Equation for cars: y = 3.5(1 + 0.25)^x​

​

3.5(1 + 0.25)^x > 5.75(1 + 0.16)^x​

3.5(1.25)^x > 5.75(1.16)^x​

3.5(1.25)^x > 5.75(1.16)^x​

(1.25)^x / (1.16)^x > 5.75/3.5​

(1.25 / 1.16)^x > 1. 64285714286​

x * In (1.25 / 1.16) > In (1.64285714286) <--- I removed an exponent you didn't mean here​

x > In(1.64285714286/In(1.25/1.16) <--- okay because In(1.25/1.16)>0​

x > 6.6436473051​

In approximately 6.644 years, the sale of cars will be more than the sale of motorcycles.​

This looks good. I hope you paid attention to the fact that you could safely divide only because the divisor was positive.

 

[rachelmaddie]

Here is what you wrote, with exponents indicated properly (using the [MATH]x^2[/MATH] button on the edit bar):

Apply the growth formula to find when the sale of cars will be more than the sale of motorcycles.​

y = a (1 + r)^x​

where, a = initial amount, r = growth rate as a decimal, x = number of time intervals passed (days, months, years), and y = amount after x time​

Equation for motorcycles: y = 5.75(1 + 0.16)^x​

Equation for cars: y = 3.5(1 + 0.25)^x​

​

3.5(1 + 0.25)^x > 5.75(1 + 0.16)^x​

3.5(1.25)^x > 5.75(1.16)^x​

3.5(1.25)^x > 5.75(1.16)^x​

(1.25)^x / (1.16)^x > 5.75/3.5​

(1.25 / 1.16)^x > 1. 64285714286​

x * In (1.25 / 1.16) > In (1.64285714286) <--- I removed an exponent you didn't mean here​

x > In(1.64285714286/In(1.25/1.16) <--- okay because In(1.25/1.16)>0​

x > 6.6436473051​

In approximately 6.644 years, the sale of cars will be more than the sale of motorcycles.​

This looks good. I hope you paid attention to the fact that you could safely divide only because the divisor was positive.

Is this better??
Apply the growth formula to find when the sale of cars will be more than the sale of motorcycles.
y = a (1 + r)^x
where, a = initial amount, r = growth rate as a decimal, x = number of time intervals passed (days, months, years), and y = amount after x time
Equation for motorcycles: y = 5.75(1 + 0.16)^x
Equation for cars: y = 3.5(1 + 0.25)^x

3.5(1 + 0.25)^x > 5.75(1 + 0.16)^x
3.5(1.25)^x > 5.75(1.16)^x
3.5(1.25)^x > 5.75(1.16)^x
(1.25)^x / (1.16)^x > 5.75/3.5
(1.25 / 1.16)^x > 1. 64285714286
x * In (1.25 / 1.16) > In (1.64285714286)
x > In(1.64285714286/In(1.25/1.16)>0
x > 6.6436473051
In approximately 6.644 years, the sale of cars will be more than the sale of motorcycles.

 

[Dr.Peterson]

See comments inside quote:

Is this better??
Apply the growth formula to find when the sale of cars will be more than the sale of motorcycles.
y = a (1 + r)^x
where, a = initial amount, r = growth rate as a decimal, x = number of time intervals passed (days, months, years), and y = amount after x time
Equation for motorcycles: y = 5.75(1 + 0.16)^x
Equation for cars: y = 3.5(1 + 0.25)^x

3.5(1 + 0.25)^x > 5.75(1 + 0.16)^x
3.5(1.25)^x > 5.75(1.16)^x
3.5(1.25)^x > 5.75(1.16)^x <-- why didn't you remove the duplicate line?
(1.25)^x / (1.16)^x > 5.75/3.5
(1.25 / 1.16)^x > 1. 64285714286
x * In (1.25 / 1.16) > In (1.64285714286)
x > In(1.64285714286/In(1.25/1.16)>0 <-- the ">0" doesn't belong here
x > 6.6436473051
In approximately 6.644 years, the sale of cars will be more than the sale of motorcycles.