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Katena32 [7]
3 years ago
12

The formula Upper A equals 23.1 e Superscript 0.0152 tA=23.1e0.0152t models the population of a US​ state, A, in​ millions, t ye

ars after 2000.
a. What was the population of the state in​ 2000?
b. When will the population of the state reach 28.328.3 ​million?
Mathematics
1 answer:
Wewaii [24]3 years ago
3 0

Answer:

a) A(t=0)= 23.1 e^{0.0152(0)}=23.1e^0 =23.1

b) t = \frac{ln(\frac{28.3}{23.1})}{0.0152}=13.357 years

So for this case the answer would be 13.347 years, the population will be 28.3 million and ye year would be 2000+13.347 and that would be approximately in 2014

Step-by-step explanation:

For this case we assume the following model:

A(t)= 23.1 e^{0.0152 t}

Where t is the number of years after 2000/

Part a

For this case we want the population for 2000 and on this case the value of t=0 since we have 0 years after 2000. If we rpelace into the model we got:

A(t=0)= 23.1 e^{0.0152(0)}=23.1e^0 =23.1

So then the initial population at year 2000 is 23.1 million of people.

Part b

For this case we want to find the time t whn the population is 28.3 million.

So we need to solve this equation:

28.3= 23.1 e^{0.0152(t)}

We can divide both sides by 23.1 and we got:

\frac{28.3}{23.1}= e^{0.0152t}

Now we can apply natural log on both sides and we got:

ln(\frac{28.3}{23.1})= 0.0152 t

And then for t we got:

t = \frac{ln(\frac{28.3}{23.1})}{0.0152}=13.357 years

So for this case the answer would be 13.347 years, the population will be 28.3 million and ye year would be 2000+13.347 and that would be approximately in 2014

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