Math Question

[Chinch]

I'm going crazy here its probably an easy question but I thought i'd ask BG haha.

Its an Econ growth question.. Wants you to find in how many years will these two countries have equal per capita GDP..

Va(t) = 50000e^0.3t is country A

Vb(t) = 25000e^0.8t is country B


I dunno am I dumb or something lol have a go at it....


t is years

[Eliseos]

Set them equal to eachother and solve for t?

[Drex]

Since it just wants to know how many times they are equal and not when, you could just graph them both and count the intersections. Wolfram says 1, at about 1.39 years.

[Chinch]

i've tried equating but I dont know whats wrong.. don't seem to be getting a right answer.

[Kaylia]

I'm going crazy here its probably an easy question but I thought i'd ask BG haha.

Its an Econ growth question.. Wants you to find in how many years will these two countries have equal per capita GDP..

Va(t) = 50000e^0.3t is country A

Vb(t) = 25000e^0.8t is country B


I dunno am I dumb or something lol have a go at it....


t is years

This is about as easy as it can get.

What you're looking for is when the capita GDP of one will equal the capita GDP of the other. So, when Va(t) is going to be equal to Vb(t)

Va(t) = Vb(t)
50000e^0.3t = 25000e^0.8t

This can be solved easily if you know how to divide exponential number with the same base, and know how to use the log function.

[Chinch]

Haha, I know it should be easy.. Its okay though, I'm sure I'll get it eventually it was just getting my frustrated because it wasn't working for me.

[BerenTebogo]

2 = (e^.8t / e^.3t) simplify and ln both sides. Look up rules for shit because google.

[Woozie]

50000e^0.3t = 25000e^0.8t iff
ln(50000e^.3t) = ln(25000e^.8t) iff
ln(50000) + .3t = ln(25000) + .8t iff
ln(50000)-ln(25000) = .5t iff
ln(50000/25000) = .5t iff
ln(2) = .5t iff
t=2*ln(2) = ln(4)=1.38629436

[Maguspk]

I feel like I haven't seen Woozie post in years, it's like running into an old friend.

Spoiler: show

who really likes physics