# Exponential Problem

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Hi! Can someone please help me with this question I've attached. I don't understand how I can prove b to = 20 and the mark scheme is confusing me even more. Many thanks

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(Original post by

what have you done so far?

**Bexr**)what have you done so far?

and 331 = ae^0.1 +be^0.2

then ae^0.1 = be^0.2 /290

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#4

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)

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#5

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.

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#6

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.

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.

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(Original post by

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.

**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.

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(Original post by

Thank you! That helped so much

**Hollymae764**)Thank you! That helped so much

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?

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#9

(Original post by

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?

**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?

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

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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?

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?

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#11

If should be:

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

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

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

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

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#12

(Original post by

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?

**Hollymae764**)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?

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#13

The way that old_engineer suggests is the easiest method - multiply the first simple equation by e^0.1 and then subtract one from the other to eliminate "a"

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(Original post by

If should be:

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

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

**mathstutor24**)If should be:

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

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

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