Exponential Problem

what have you done so far?

Reply 2

OP

Original post by Bexr

what have you done so far?

I got 290 = a + b
and 331 = ae^0.1 +be^0.2

then ae^0.1 = be^0.2 /290

Reply 3

username4197954

Yep - good! So .... rather than rearrange the 2nd equation, think about the b value you are trying to prove and how you can rewrite the second equation with just b. (HINT look at the first "simple" equation)

Reply 4

old_engineer

Original post by Hollymae764

I got 290 = a + b
and 331 = ae^0.1 +be^0.2

then ae^0.1 = be^0.2 /290

The first two equations are correct, but the third one is wrong.
I would suggest multiplying the first equation (all terms) by e^0.1, then subtracting one equation from the other to eliminate a and leave b.

Reply 5

username4197954

I was trying to get you to spot that if you rewrite the first equation as
a = 290-b
you can then sub this into the 2nd equation, which will give eliminate "a" and allow you to rearrange to find "b".

In any case, by creating the 2 equations you now have simultaneous equations, so you can use your favourite method to solve them.

Reply 6

OP

Original post by Bexr

I was trying to get you to spot that if you rewrite the first equation as
a = 290-b
you can then sub this into the 2nd equation, which will give eliminate "a" and allow you to rearrange to find "b".

In any case, by creating the 2 equations you now have simultaneous equations, so you can use your favourite method to solve them.

Thank you! That helped so much :smile:

Reply 7

OP

Original post by Hollymae764

Thank you! That helped so much :smile:

I'm kind of stuck again, so I rearranged them

ae^0.1t = be^0.2t -290

then I put this into the other equation

331 = (be^0.2t -290) + be^0.2t
621 = 2be^0.2t

I don't know what to do from here is this even correct?

Reply 8

davros

16

Original post by Hollymae764

I'm kind of stuck again, so I rearranged them

ae^0.1t = be^0.2t -290

then I put this into the other equation

331 = (be^0.2t -290) + be^0.2t
621 = 2be^0.2t

I don't know what to do from here is this even correct?

You seem to have got a bit muddled with the algebra!

Remember that your second equation (for 2018) comes from when t = 1 so you shouldn't have any t's left in your final equations.

You found that a + b = 290 so that a = 290 - b. What do you get first of all when you substitute this into

331 = ae^{0.1} + be^{0.2}

Reply 9

OP

I did:

331 = 290 - be^0.1 + be^0.2
41 = -be^0.1 +be^0.2
41 = -b (e^0.1 - e^0.2)
41/(e^0.1 - e^0.2) = -b
b = 352.74

What have I done wrong?

Reply 10

mathstutor24

9

If should be:

331 = (290-b)e^0.1 + be^0.2

(You've subbed in "a" without using brackets)

Reply 11

old_engineer