202,000=32,800e^k*20 - Solve for K

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In summary, the conversation involved solving the equation 202,000=32,800e^k*20 for k. The suggested method was to use ln and isolate the e^x term, resulting in the solution k = (ln(202,000/32800)/20). It was also noted that writing e^(20k) would be clearer to show the intended order of operations.
  • #1

Homework Statement


Did most the problem, but know I'm stuck here: 202,000=32,800e^k*20

I need to solve for K

The Attempt at a Solution



Log 202,000 = k*20 log 32,000 e

Do you move the e out in front too? I'm not sure, anyway, I'm stuck here. Not sure what to do or even if you use logs to solve for k.
 
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  • #2
killersanta said:

Homework Statement


Did most the problem, but know I'm stuck here: 202,000=32,800e^k*20

I need to solve for K

The Attempt at a Solution



Log 202,000 = k*20 log 32,000 e

Do you move the e out in front too? I'm not sure, anyway, I'm stuck here. Not sure what to do or even if you use logs to solve for k.

Remember to use "ln" and not "log" for the inverse operation of [tex]e^x[/tex]

So if you isolate the [tex]e^x[/tex] term, it looks more like this:

[tex]\frac{202000}{32800} = e^{k*20} [/tex]

What would you now do to get rid of the exponential issue so you can deal directly with k?

BTW, I assume this is the end of a calculus problem, with the end not involving calculus.
 
  • #3
berkeman said:
Remember to use "ln" and not "log" for the inverse operation of [tex]e^x[/tex]

So if you isolate the [tex]e^x[/tex] term, it looks more like this:

[tex]\frac{202000}{32800} = e^{k*20} [/tex]

What would you now do to get rid of the exponential issue so you can deal directly with k?

BTW, I assume this is the end of a calculus problem, with the end not involving calculus.

LN(202,000/32800)= K * 20

k = (LN(202,000/32800)/20) = .09089 ?
 
  • #4
That works for me.

Be advised, though, that most people would read e^k*20

as ek * 20, and not as e20k, as I think you intended. To better show your intent, write that part as e^(20k). Then it's clear what is in the exponent.
 
  • #5
Mark44 said:
That works for me.

Be advised, though, that most people would read e^k*20

as ek * 20, and not as e20k, as I think you intended. To better show your intent, write that part as e^(20k). Then it's clear what is in the exponent.

Sweet, Thanks... And I will do from now on.
 

1. What is the equation "202,000=32,800e^k*20" trying to solve for?

The equation is trying to solve for the value of k.

2. How can I solve for k in the equation "202,000=32,800e^k*20"?

To solve for k, you can use algebraic manipulation to isolate the variable k on one side of the equation.

3. What is the significance of the number 20 in the equation "202,000=32,800e^k*20"?

The number 20 represents the number of years in the exponential growth model being used in the equation.

4. Can this equation be solved using a calculator?

Yes, this equation can be solved using a calculator by using the natural logarithm function to solve for k.

5. What are the units of measurement for the value of k in the equation "202,000=32,800e^k*20"?

The units of measurement for k will depend on the units used for the other values in the equation. If all values are in years, then k will also be measured in years.

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