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applying differential equations to real-life problems

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Original post by Alen.m

So basically it's a graph of y=30000-20000e^0.2tIn(0.9)? The reason im asking is because the text book stated it's a graph of e^0.2In(0.9t) which should definetely be different

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It's sloppy notation on their part, what they mean is

e^{0.2 \ln (0.9) t}

OP

Original post by Zacken

It's sloppy notation on their part, what they mean is

e^{0.2 \ln (0.9) t}

how about if i wanna sketch the graph of y=30000-20000e^0.2In(0.9t), in this case actually as t increases the value of e^0.2In(0.9t) increases as well therefore the value of c will decrease and the graph would look like something like this?

12822600_1991620097728984_1648905777_o.jpg210.2KB

Original post by Alen.m

how about if i wanna sketch the graph of y=30000-20000e^0.2In(0.9t), in this case actually as t increases the value of e^0.2In(0.9t) increases as well therefore the value of c will decrease and the graph would look like something like this?

Not quite, if you wanted to sketch that graph, as soon as

t > 1.12

, the value for the exponential becomes positive, which makes

20 000 e^{\text{blah}} >> 30,000

so your whole thing becomes negative. It would look like this:

OP

Original post by Zacken

Not quite, if you wanted to sketch that graph, as soon as

t > 1.12

, the value for the exponential becomes positive, which makes

20 000 e^{\text{blah}} >> 30,000

so your whole thing becomes negative. It would look like this:

thanks

OP

Original post by Zacken

Not quite, if you wanted to sketch that graph, as soon as

t > 1.12

, the value for the exponential becomes positive, which makes

20 000 e^{\text{blah}} >> 30,000

so your whole thing becomes negative. It would look like this:

how about before 1.12 tho? the value of c getting smaller and smaller until t reaches 1.12 then it gets negative ?

Original post by Alen.m

how about before 1.12 tho? the value of c getting smaller and smaller until t reaches 1.12 then it gets negative ?

Yep.

OP

Original post by Zacken

Yep.

Shouldnt it be something like this tho? Coz c start getting negative as t reaches 1.12 but on yours c is already negative before 1.12

Original post by Alen.m

Shouldnt it be something like this tho? Coz c start getting negative as t reaches 1.12 but on yours c is already negative before 1.12

That's correct. Look at the scale of my graph. :-)

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