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3 years ago

What is the value of r in this equation for exponential growth?

Mathematics

1 answer:

puteri [66]3 years ago

8 0

Answer:

$r=0.75 = 75$ %

Step-by-step explanation:

Equation of General exponential growth function is

$f(x)=a(1+r)^{x}$ ------------ (1)

Where a is initial value x is time and r is growth rate

Given function can be written in following form

$f(x)=2500(1+0.75)^{x}$ ------------ (2)

After comparing (1) and (2) we can conclude that

$r=0.75 = 75$ %

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Use the position function s(t) = –16t2 + 800, which gives the height (in feet) of an object that has fallen for t seconds from a

Ostrovityanka [42]

Answer:

96 ft/s

Step-by-step explanation:

We can start by deriving the equation of the velocity, which is the derivative of the position equation:

$v(t) = \frac{ds}{dt} = (-16t^2)' + 800' = -32t$

After 3 seconds, the wrench would achieve a speed of

v(3) = -32t = -32*3 = -96 ft/s

So it's falling at the rate of 96 ft per second after 3 s

4 0

4 years ago

How do i verify? (1-cos^2 x)(1+tan^2 x)=tan^2 x

andre [41]

Answer:

(1-cos^2 x)(1+tan^2 x)=tan^2 x is an identity

Step-by-step explanation:

use pictomath

7 0

4 years ago

A well known pharmaceutical manufacturer is manufacturing a newly developed vaccine, and is concerned about variability in the i

Lana71 [14]

Answer:

The null hypothesis is $H_o : \ \sigma^2 = 1.9$

The alternative hypothesis is $H_a : \ \sigma^2 \ne 1.9$

$X^2 = 13.74$

The decision rule is

Reject the null hypothesis

The conclusion is

There is no sufficient evidence to conclude that the variance of the immune response is equal to 1.9.

Step-by-step explanation:

From the question we are are told that

The variance is $\sigma ^2 = 1.9$

The sample size is n = 30

The sample variance is $s^2 = 0.9$

The level of significance is $\alpha = 0.05$

The null hypothesis is $H_o : \ \sigma^2 = 1.9$

The alternative hypothesis is $H_a : \ \sigma^2 \ne 1.9$

Generally the test statistics is mathematically represented as

$X^2 = \frac{ (n- 1 ) * s^2 }{ \sigma^2 }$

=> $X^2 = \frac{ (30 - 1 ) * 0.9 }{1.9 }$

=> $X^2 = 13.74$

Generally from the degree of freedom is mathematically represented as

$df = n- 1$

=> $df = 30 - 1$

=> $df = 29$

Generally from the chi distribution table the critical value of $\frac{\alpha}{2} \ and \ 1 - \frac{ \alpha }{2}$ at a degree of freedom of $df = 29$ is

$X^2 _{ \frac{\alpha }{2} , df } = X^2 _{ \frac{0.05 }{2} , 29 } = 45.7$

=> $X^2 _{ 1 - \frac{\alpha }{2} , df } = X^2 _{1 - \frac{0.05 }{2} , 29 } = 16.0 5$

Gnerally from the values obtained we see that

$X^2 < X^2 _{ 1 - \frac{\alpha }{2} , df }$ hence

The decision rule is

Reject the null hypothesis

The conclusion is

There is no sufficient evidence to conclude that the variance of the immune response is equal to 1.9.

6 0

3 years ago

Which set of points would result in a slope of 1/4

8090 [49]

Answer:

C) ( 8,2) and (4,1)

The slope of the line

$m = \frac{1}{4}$

Step-by-step explanation:

Explanation:-

Given that the set of points ( 8,2) and (4,1)

ThesSlope of the line

$m = \frac{y_{2}-y_{1} }{x_{2} -x_{1} }$

$m = \frac{1-2 }{4-8 }= \frac{-1}{-4} = \frac{1}{4}$

The slope of the line

$m = \frac{1}{4}$

4 0

3 years ago

Solve the system of equations by the addition method.

Eva8 [605]

$\left \{ {{\frac{x}{2}-y=7 } \atop {-\frac{x}{7}+\frac{2y}{7}= -2 }} \right. \left \{ {{\frac{x}{2}.2-2y=2.7} \atop {-\frac{x}{7}.7+\frac{2y}{7}.7= -2.7}} \right. \left \{ {{x-2y=14} \atop {-x+2y=-14}} \right. \left \{ {{0x=0} \atop {y={\frac{x}{2}-7}} \right.$

ANSWER: B

ok done. Thank to me :>

8 0

3 years ago

Read 2 more answers