Exponential functions word problem

[Coco12]

Homework Statement

The function T=190(1/2)^1/10t can be used to determine the length of time t, in hrs that milk will remain fresh. T is the storage temp. In Celsius
How long will milk remain fresh at 22 degrees Celsius

Homework Equations

Bases have to be same then exponents will equal one another

The Attempt at a Solution

In this equation , we need to solve for the t in the exponent. I thought you has to divide 22 (T) by 190 and tried to make it so that the base is the same as (1/2) but the number when you divide 22 by 190 is a very long decimal and I don't know how to do that. So far we have not done Logs yet in class so how can I solve that without using logs?

 

[SteamKing]

Homework Statement

The function T=190(1/2)^1/10t can be used to determine the length of time t, in hrs that milk will remain fresh. T is the storage temp. In Celsius
How long will milk remain fresh at 22 degrees Celsius

Homework Equations

Bases have to be same then exponents will equal one another

The Attempt at a Solution

In this equation , we need to solve for the t in the exponent. I thought you has to divide 22 (T) by 190 and tried to make it so that the base is the same as (1/2) but the number when you divide 22 by 190 is a very long decimal and I don't know how to do that. So far we have not done Logs yet in class so how can I solve that without using logs?

"Bases have to be same then exponents will equal one another"

It's unclear what this statement means, and I don't think it will help solve the problem.

Don't you understand how logarithms work? Try taking the logarithm of both sides of the Temperature equation.

Remember that e^(ln x) = x

 

[HallsofIvy]

Homework Statement

The function T=190(1/2)^1/10t can be used to determine the length of time t, in hrs that milk will remain fresh. T is the storage temp. In Celsius
How long will milk remain fresh at 22 degrees Celsius

Homework Equations

Bases have to be same then exponents will equal one another

The Attempt at a Solution

In this equation , we need to solve for the t in the exponent. I thought you has to divide 22 (T) by 190 and tried to make it so that the base is the same as (1/2) but the number when you divide 22 by 190 is a very long decimal and I don't know how to do that. So far we have not done Logs yet in class so how can I solve that without using logs?

Surely you are not going to let a number, even a very long one, scare you? The fact that you have not done logarithms is more important. 22/190= 0.115789, approximately, and if I don't want to (or can't) use logarithms then I had better think in terms of powers of 1/2. I know that $(1/2)^3= 1/8= 0.125$ and $(1/2)^4= 1/16= 0.0625$ so the nearest I can do is that 1/(10t) is about 3.

 

[BruceW]

yes, without using logarithms, the simplest method is probably the tried-and-tested, backup-option of just trying a few values, and choosing the one that fits the equation the closest.

 

[Coco12]

Ok thank you , could I also use a graphing calculator?

 

[BMW]

Is the exponent (1/10)t or 1/(10t) ? Also you can press the little X² button to do exponents properly.

 

[BruceW]

@Coco12: yeah, that should work. when it draws the graph of the function, it will essentially do the same thing you are (i.e. choose a bunch of values and calculate what the function evaluates to). except it will generally be faster than a person. be careful to avoid t=0

 

[Mark44]

Is the exponent (1/10)t or 1/(10t) ? Also you can press the little X² button to do exponents properly.

To get to that extended menu, click Go Advanced. The X² let's you enter exponents so they appear in a nice format.