QuestionFind the population of a city in the Philippines after 20 years using the model $A=50 e^{0.07 t}$ .

Studdy Solution

STEP 1

Assumptions1. The population growth model is $A=50 e^{0.07 t}$ . The population is measured in thousands3. $t$ is the time in years after1997

STEP 2

To find the population after20 years, we need to substitute $t=20$ into the exponential growth model.
$A =50 e^{0.07 \times20}$

STEP 3

First, calculate the exponent.
$0.07 \times20 =1.$ So, the equation becomes $A =50 e^{1.}$

STEP 4

Now, calculate the value of $e^{1.4}$ .
$e^{1.4} \approx4.0552$ So, the equation becomes $A =50 \times4.0552$

STEP 5

Finally, calculate the population after20 years.
$A =50 \times4.0552 =202.76$ The population of the city in the Philippines after20 years is approximately202,760 (since the population is measured in thousands).

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QuestionFind the population of a city in the Philippines after 20 years using the model $A=50 e^{0.07 t}$ .

Studdy Solution

STEP 1

Assumptions1. The population growth model is $A=50 e^{0.07 t}$ . The population is measured in thousands3. $t$ is the time in years after1997

STEP 2

To find the population after20 years, we need to substitute $t=20$ into the exponential growth model.
$A =50 e^{0.07 \times20}$

STEP 3

First, calculate the exponent.
$0.07 \times20 =1.$ So, the equation becomes $A =50 e^{1.}$

STEP 4

Now, calculate the value of $e^{1.4}$ .
$e^{1.4} \approx4.0552$ So, the equation becomes $A =50 \times4.0552$

STEP 5

Finally, calculate the population after20 years.
$A =50 \times4.0552 =202.76$ The population of the city in the Philippines after20 years is approximately202,760 (since the population is measured in thousands).

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QuestionFind the population of a city in the Philippines after 20 years using the model A=50e0.07tA=50 e^{0.07 t}A=50e0.07t.

Studdy Solution

STEP 1

Assumptions1. The population growth model is A=50e0.07tA=50 e^{0.07 t}A=50e0.07t . The population is measured in thousands3. ttt is the time in years after1997

STEP 2

To find the population after20 years, we need to substitute t=20t=20t=20 into the exponential growth model.A=50e0.07×20A =50 e^{0.07 \times20}A=50e0.07×20

STEP 3

First, calculate the exponent.0.07×20=1.0.07 \times20 =1.0.07×20=1.So, the equation becomesA=50e1.A =50 e^{1.}A=50e1.

STEP 4

Now, calculate the value of e1.4e^{1.4}e1.4.e1.4≈4.0552e^{1.4} \approx4.0552e1.4≈4.0552So, the equation becomesA=50×4.0552A =50 \times4.0552A=50×4.0552

STEP 5

Finally, calculate the population after20 years.A=50×4.0552=202.76A =50 \times4.0552 =202.76A=50×4.0552=202.76The population of the city in the Philippines after20 years is approximately202,760 (since the population is measured in thousands).

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QuestionFind the population of a city in the Philippines after 20 years using the model $A=50 e^{0.07 t}$ .

Assumptions1. The population growth model is $A=50 e^{0.07 t}$ . The population is measured in thousands3. $t$ is the time in years after1997

To find the population after20 years, we need to substitute $t=20$ into the exponential growth model.
$A =50 e^{0.07 \times20}$

First, calculate the exponent.
$0.07 \times20 =1.$ So, the equation becomes $A =50 e^{1.}$

Now, calculate the value of $e^{1.4}$ .
$e^{1.4} \approx4.0552$ So, the equation becomes $A =50 \times4.0552$

Finally, calculate the population after20 years.
$A =50 \times4.0552 =202.76$ The population of the city in the Philippines after20 years is approximately202,760 (since the population is measured in thousands).