Value of "e" question

[super_chris1234]

Hello,
This question in my text book has been giving me some problems as I am not fully aware how to solve equations with the value of "e"

The population growth of mosquitoes, M, in a certain tropical zone, Shamagala, at time t(in hours) is given by

M(t)=1000e^t/60.
a) How many mosquitoes are in Shamagala at t=0 hours?

What I initially thought to do is set t=0 and solve for e: M(t)=1000e^0/60.
But, I'm completely dumfounded on how to solve this question.


Thank you very much,

Chris

 

[Deleted member 4993]

Hello,
This question in my text book has been giving me some problems as I am not fully aware how to solve equations with the value of "e"

The population growth of mosquitoes, M, in a certain tropical zone, Shamagala, at time t(in hours) is given by

M(t)=1000e^t/60.
a) How many mosquitoes are in Shamagala at t=0 hours?

What I initially thought to do is set t=0 and solve for e: M(t)=1000e^0/60.
But, I'm completely dumfounded on how to solve this question.


Thank you very much,

Chris

Hint:

for \(\displaystyle x \ne 0\)


\(\displaystyle \frac{0}{x} \ = \ 0\)

and

for \(\displaystyle a \ne 0\)

\(\displaystyle a^0 \ = \ 1\)

 

[super_chris1234]

Thanks, so the correct way to approach and solve would be as indicated below

M(t)=1000e^0/60

M(t)=1000e¹

M(t)1000(2.7178)¹

M(t)=2717.8 mosquitoes

Any feed back regarding my method is greatly appreciated.

Chris

 

[Deleted member 4993]

No......

Thanks, so the correct way to approach and solve would be as indicated below

M(0)=1000*e^0/60

M(0)=1000*e⁰

M(0)=1000*1
M(0)=1000 mosquitoes

Any feed back regarding my method is greatly appreciated.

Chris

 

[super_chris1234]

Thanks for your help. Now, when finding a value for population after a set period of time, I.E. 20 hours, how would I approach that?

My initial thoughts are as follows:

M(20)=1000e^20/60

Then just simplify. But, I'm not sure if this is the best option

Thanks for the help

 

[Deleted member 4993]

Thanks for your help. Now, when finding a value for population after a set period of time, I.E. 20 hours, how would I approach that?

My initial thoughts are as follows:

M(20)=1000e^20/60

Then just simplify. .........YES

But, I'm not sure if this is the best option

Thanks for the help

.

 

[super_chris1234]

---

Thanks, but when I plug it into my calculator, I get 1.6666667e58. That doesn't seem right. Something tells me I'm doing this wrong. Any help would be greatly appreciated. Thanks again

 

[srmichael]

---

\(\displaystyle \displaystyle M(t)=1000e^{\frac{t}{60}}\)

Initial Amount is at t=0: \(\displaystyle \displaystyle M(0)=1000e^{\frac{0}{60}}=1000\)

Amount at t=20 hours: \(\displaystyle \displaystyle M(20)=1000e^{\frac{20}{60}}\approx1396\)

Make sure when you type 20/60 in your calculator you put parentheses around it otherwise the calcualtor will do 1000e^20 first then divide by 60.

 

[super_chris1234]

Thank you very much. As I thought, it was a calculator error.

 

[Deleted member 4993]

No... it was an OPERATOR error.

Calculatots generally do not make mistake - Garbage in → Garbage out.

 

[super_chris1234]

Thanks. Now, how would I find out how long it takes for the value of mosquitoes to double?
This is what I tried so far:
2000(t)=1000e^t/60
log2000(t)=log1000e^t/60
log2000(t)=60log1000e^t

But, this is where I get stuck. Any help would be greatly appreciated!

 

[Deleted member 4993]

Thanks. Now, how would I find out how long it takes for the value of mosquitoes to double?
This is what I tried so far:
2000(t)=1000e^t/60
log2000(t)=log1000e^t/60
log2000(t)=60log1000e^t

But, this is where I get stuck. Any help would be greatly appreciated!

You need to review your logarithm skills....

2 = e^t/60

ln(2) = t/60 → t = 60* ln(2)

Now continue....

Note: ln(2) = log_e(2)

 

[super_chris1234]

Thank you! My text book never specified about natural logarithms so that's what confused me. Thanks again! But, what happened to the 1000e?

 

[Deleted member 4993]

Thank you! My text book never specified about natural logarithms so that's what confused me. Thanks again! But, what happened to the 1000e?

2000 / 1000 = 2