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Umnica [9.8K]
2 years ago
10

The current population of a town is 8,000. If the population, P, increases by 25% each year, which equation could be used to fin

d the population after t years?
Mathematics
1 answer:
Bad White [126]2 years ago
4 0

Answer:

given:

principal [P]=8000

rate[r]=15%

population after t years=?

we have

population after t years=P(1+r/100)^t=8000(1+15/100)^t is your answer

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Exponential function f is represented by the table. x -2 -1 0 1 2 f(x) -46 -22 -10 -4 -1 Function g is represented by the equati
Scrat [10]

The statement that describes better about function is "Both functions are increasing, but function g increases at a faster average rate." since option (c) is correct.

Given the table

x         f(x)

-2        -46

-1         -22

0         -10

1           -4

2          -1

We have to choose which statement describes better about function

Let us assume f(x)=ab^x+c

at x=0, f(0)=-10

So, -10 =a+c

Similarly, by satisfying the above table in the f(x)

f(x)=\frac{33}{5} (\frac{1}{11})^x-\frac{17}{5}

f'(x) > 0

So we can say that f(x) is an increasing function.

g(x) = - 18  (\frac{1}{3}  )^ x + 2

g^ \prime (x) = - 18 (\frac{1}{3}  )^ x  ln(1/3)

ln(1/3) < 0

So, g^ \prime (x) > 0

So, g(x) is an increasing function.

For any x∈f(x) and  x∈g(x) g'(x) > f'(x)

So, g increases at a faster average rate

Thus, Both functions are increasing, but function g increases at a faster average rate.

Learn more about increasing functions here: brainly.com/question/12940982

#SPJ10

7 0
1 year ago
Please help! I will mark as brainliest IF answer is right. &lt;3
weeeeeb [17]
Hope this helps. :D
(Please mark as brainliest thanks)

8 0
3 years ago
a researcher at a major clinic wishes to estimate the proportion of the adult population of the united states that has sleep dep
Anna11 [10]

Answer:

The estimate of a population proportion is approximately 541.

Step-by-step explanation:

We can solve the the problem by using the formula for minimum sample needed for interval estimate of a population proportion which is given by the formula

n = pq ((Z/2) / E)^2

As, p is not defined so we use the standard p and q which is 0.5 and 0.5.

The reason for this is we have to choose form 0.1 to 0.9 both values of p and q, we will find the maximum value of pq occurs when they both are 0.5.

Next, we will find the value of (Z/2) by looking at the Z-table, we will find that at 98% confidence (Z/2) = 2.326. Now we start substituting the values in the above formula

n = (0.5)×(0.5) × (2.326/0.05)^2

n = 541.027

n ≅ 541.

5 0
3 years ago
7 + 24 .3<br> 31<br> 55<br> c<br> 96<br> 112
GaryK [48]

Answer:

The answer is 325.3

Step-by-step explanation:

I hope this helped I used a calculator sorry if I'm late and I hope this isn't wrong

7 0
2 years ago
Prove this trigonometric equation;<br><br> - tan^2x + sec^2x = 1,
alekssr [168]
Hey there :)

- tan²x + sec²x = 1    or    1 + tan²x = sec²x

sin²x + cos²x = 1 
Divide the whole by cos²x

\frac{sin^2x}{cos^2x} + \frac{cos^2x}{cos^2x} = \frac{1}{cos^2x}

\frac{sinx}{cosx} = tanx so \frac{sin^2x}{cos^2x} = tan^2x
and
\frac{1}{cosx} = secx so \frac{1}{cos^2x} = sec^2x

Therefore,
tan²x + 1 = sec²x
Take tan²x to the other side {You will have the same answer}

1 = - tan²x = sec²x or sec²x - tanx = 1

3 0
2 years ago
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