Ju2lismbr9okebrucha
contestada

Since January 1, 1960, the population of Slim Chance has been described by the formula P=33000(0.98)^t where P is the population of the city t years after the start of 1960. At what rate was the population changing on January 1, 1978?

Respuesta :

calculista

Let

P-------> the population of Slim Chance (Since January 1, 1960)

t--------> the number of years (after the start of 1960)

we know that

[tex]P=33,000*(0.98)^{t}[/tex]

Step 1

Take the derivative of P with respect to t

[tex]\frac{dP}{dt}=33,000*(0.98)^{t}*ln(0.98)[/tex]

Step 2

[tex]1978-1960=18\ years[/tex]

Evaluate the derivative of P with respect to t for [tex]t=18\ years[/tex]

substitute

[tex]\frac{dP}{dt}=33,000*(0.98)^{18}*ln(0.98)=-463.44\frac{people}{year}[/tex]

therefore

the answer is

The rate of change is [tex]-463.44 \frac{people}{year}[/tex]



abiolataiwo2015

If  January 1, 1960, the population of Slim Chance has been described by the formula P=33000(0.98)^t where P is the population of the city t years after the start of 1960. The rate that the population change on January 1, 1978 is : 22,940

Let P=33000(0.98)^t

Let t = 18 (1978-1960)

Now let determine at what rate was the population changing on January 1, 1978

Change in population = 33000(0.98)^18

Change in population= 22,939.47

Change in population=22,940 (Approximately)

 

Inconclusion if  January 1, 1960, the population of Slim Chance has been described by the formula P=33000(0.98)^t where P is the population of the city t years after the start of 1960. The rate that the population change on January 1, 1978 is : 22,940

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