SOLUTION: Hello, I need help with an exponential growth model word problem : The population of Houston Texas was 2.30 million in 1990, and 2.65 million in 2000. Using an exponential growth

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Question 425275: Hello, I need help with an exponential growth model word problem :
The population of Houston Texas was 2.30 million in 1990, and 2.65 million in 2000. Using an exponential growth model, +y+=+ne%5Ekt+, sketch a graph of the population beginning in 1990 and find the predicted population in 2010
I checked my exponential growth notes but the formula was not the same it is: +y+=+a+sqrt%28+x-h+%29+%2B+k+ and we found the vertex from that (which is the "h" and "k"), then made our graphs. I checked online and there was a calculater for it and that gave me an answer of 76.16554 which I do not think has anything to do with this question. Thank you so much for your time.
Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
The population of Houston Texas was 2.30 million in 1990,
and 2.65 million in 2000. Using an exponential growth model, y = ne^kt , sketch a graph of the population beginning in 1990 and find the predicted population in 2010
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In 2000 t is 10
2.65 = n*e^10k
In 1990 t is zero.
2.30 = n*e^0
---
So n = 2.30
---
So 2.65 = 2.30*e^10k
---
So e^10k = 1.152174
Take the natural log of both sides to get:
10k = 0.141651
k = 0.014165
---
Equation:
y = 2.30*e^(0.014165t)
find the predicted population in 2010
In 2010 t = 20
y = 2.30*e^(0.014165*20)
y = 3.053258 million
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Graph:
graph%28400%2C300%2C-5%2C25%2C-5%2C5%2C2.30%2A%282.718281828%29%5E%280.014165x%29%29
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Cheers,
Stan H.
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