Mathematics, 21.10.2019 17:30 mommatann

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?

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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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Answer from: seanisom7

Let

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

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

we know that

$P=33,000*(0.98)^{t}$

Step 1

Take the derivative of P with respect to t

$\frac{dP}{dt}=33,000*(0.98)^{t}*ln(0.98)$

Step 2

$1978-1960=18\ years$

Evaluate the derivative of P with respect to t for $t=18\ years$

substitute

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

therefore

the answer is

The rate of change is $-463.44 \frac{people}{year}$

Answer from: Quest

597

step-by-step explanation:

Answer from: Quest

answer:

given the linear inequality : $x-2y\geq -12$

add 2y to both sides we get;

$x-2y+2y\geq -12+2y$

simplify:

$x\geq -12+2y$

add 12 to both sides of an equation;

$x+12\geq -12+2y+12$

simplify:

$x+12\geq 2y$

divide both sides by 2 we get;

$\frac{x}{2} + 6 \geq y$

$y\leq \frac{x}{2} + 6$

the related equation for the inequality equation [1] is;

$y =\frac{x}{2} +6$

y-intercepts defined as the graph crosses the y-axis.

substitute x =0 in [2] to solve for y;

$y =\frac{0}{2} +6$

y = 6

x-intercepts defined as the graph crosses the x-axis.

substitute value y = 0 to solve for x;

$0 =\frac{x}{2} +6$

subtract 6 from both sides we get

$0-6 =\frac{x}{2} +6-6$

$-6 =\frac{x}{2}$

multiply both sides by 2 we get;

$-6 \times 2=x$

x = -12

now, plot these point (0, 6) and (-12, 0) on graph as shown below and shade the graph below the solid line.

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