Lexi V.

asked • 04/08/22

Pre Calc Question

Convert the exponential equation 𝑄=0.35𝑒^0.7𝑡

to the form 𝑄=𝑎𝑏𝑡 and enter the values of a and b below.

a=

b=

Inactive Tutor

hi Lexi, did you find from your teacher what answer was deemed correct? thx.
Report

04/08/22

3 Answers By Expert Tutors

By:

Inactive Tutor answered • 04/08/22

Tutor
New to Wyzant

See tutors like this
See tutors like this

e.7=2 approximately

Q=.35*2t just about

Upvote • 0 Downvote
More
Report

Inactive Tutor

Just my own two cents, but I don't think we should be encouraging students to approximate irrational numbers with integers, especially in a pre-calculus class. Before you know it, we'll have people wanting us to use 3 instead of pi everywhere. 😂 This is especially true for an exponential equation, where the margin of error will grow, well, exponentially.
Report

04/08/22

Inactive Tutor

2 to an exponent variable is doubling, If someone was trying to convert an e base equation to a doubling equation exactly, the the exponent of e would need to b= .69314718056...My two cents is the problem is pointing out the e to .7t is very much close to doubling.
Report

04/08/22

Inactive Tutor

Possibly. Maybe it's just a poor choice of question to give to a student. 🤷‍♂️
Report

04/08/22

Inactive Tutor

FWIW, the error rate grows pretty quickly. For a t value of 20, 2^t is 1048576 while (e^0.7)^t is ~1202604. That's a difference of ~154028, which is almost 13%. That's why it's not a good idea to use approximations in an exponential expression. The error rate grows really quickly.
Report

04/08/22

Inactive Tutor

agree
Report

04/08/22

Inactive Tutor answered • 04/08/22

Tutor
New to Wyzant

See tutors like this
See tutors like this

Not entirely sure what this question is asking for. Does it not like the 0.7 in the exponent and wants an equation of this form?


Q = a * bt


If so, we can rewrite our original Q equation to get there:


Q = 0.35 * e0.7*t

Q = 0.35 * (e0.7)t


So a = 0.35 and b = e0.7. e0.7 is irrational, so it can't be simplified anymore without losing precision.

Upvote • 0 Downvote
More
Report

Inactive Tutor

but e^.7=2.013752700747...,,,,,,,,,the problem wants an answer I think, not that the answer is there is no answer. Q=.35*2.013752700747^t with a high degree of accuracy.
Report

04/08/22

Inactive Tutor

Yeah, I'd throw this question back to the teacher and ask them what they're really asking for and what the point is.
Report

04/08/22

Inactive Tutor

FWIW, I think b = e^0.7 is a valid answer. It's a real number.
Report

04/08/22

Inactive Tutor

question reads"Convert the exponential equation 𝑄=0.35𝑒^0.7𝑡 to the form 𝑄=𝑎𝑏𝑡 and enter the values of a and b below." and a valid answer is there is no way to convert? The question wants the variable t not multiplied by any constant other than 1.
Report

04/08/22

Inactive Tutor

If a is 0.35 and b is e^0.7, then t just has a coefficient of 1. So this is a valid answer.
Report

04/08/22

Inactive Tutor

nothing is converted other than parentheses added. To fix any accuracy problem, e^.7 can be 2.01, or 2.013, or 2.0137,....
Report

04/08/22

Inactive Tutor

On the contrary, we are using the rules of exponents to rewrite e^(0.7*t) to (e^0.7)^t. Exponents is one of the topics that are covered in pre-calculus, so the ability to convert exponents from one form to another may be what the teacher is looking for here.
Report

04/08/22

Inactive Tutor

Also, using 2.01, 2.013, 2.0137, or ... doesn't fix the accuracy problem. It just makes the problem smaller, but the problem still exists.
Report

04/08/22

Inactive Tutor

One could also argue that Q = 0.35 * (2.01....)^t is not a valid answer because it's a different equation that gives different results. You're not converting the equation as the problem is asking, but providing a completely different equation. The only instance when your equation provides the same result is when t = 0. For all other values of t, your equation gives a different result.
Report

04/08/22

Inactive Tutor

perhaps you are right about exponent work for student. But it is also eventually important student know Ln2=about .7 (or .69 more accurately). It helps in grasping magnitude of quantities.
Report

04/08/22

Still looking for help? Get the right answer, fast.

Ask a question for free

Get a free answer to a quick problem.
Most questions answered within 4 hours.

OR

Find an Online Tutor Now

Choose an expert and meet online. No packages or subscriptions, pay only for the time you need.