Identify the rule for the following pattern: 4, 24, 144

Mathematics

1 answer:

Ivan2 years ago

7 0

Answer:

It is being multiplied by 6 each time.

Step-by-step explanation:4x6, 24x6

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The population of a small town, P, as a function of time, t, in years past 1940 is given below.

romanna [79]

Answer: 1976

Steps:

Let t* be the year in which the population reached a count of 8920. Solve for t*:

$P=200t+1720\\8920=200t^*+1720\\7200=200t^*\\t^* = 36$

The population grew to the number 8920 in 36 years past 1940, i.e., 1976

3 0

2 years ago

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Given: △ABC, m∠A=60°, m∠C=45°, AB=9 Find: Perimeter of △ABC, Area of △ABC

docker41 [41]

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3 years ago

What is the slope of the line passing thru the points (-6,-5) (4,4)

Katena32 [7]

Answer:

slope = $\frac{9}{10}$

Step-by-step explanation:

Calculate the slope m using the slope formula

m = ( y₂ - y₁ ) / ( x₂ - x₁ )

with (x₁, y₁ ) = (- 6, - 5) and (x₂, y₂ ) = (4, 4)

m= $\frac{4+5}{4+6}$ = $\frac{9}{10}$

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2 years ago

A bacteria culture initially contains 100 cells and grows at a rate proportional to its size. After an hour the population has i

bija089 [108]

Answer: $\bold{a)\ P(t)=P_o\cdot e^{t\cdot ln(2.7)}}$

b) 5314

c) ln 2.7

d) 4.6 hrs

Step-by-step explanation:

$P(t) = P_o\cdot e^{kt}\\\\\bullet \text{P(t) is the number of bacteria after t hours} \\\bullet P_o\text{ is the initial number of bacteria}\\\bullet \text{k is the rate of growth}\\\bullet \text{t is the time (in hours)}\\\\\\270=100\cdot e^{k(1)}\\2.7=e^k\\ln\ 2.7=\ln e^k\\\boxed{ln\ 2.7=k}\\\\\text{So the equation to find the number of bacteria is: }\boxed{P(t)=P_o\cdot e^{t\cdot ln(2.7)}}\\\\\\P(4)=100\cdot e^{4\cdot ln(2.7)}\\.\qquad =\boxed{5314}$

$10,000=100\cdot e^{t\cdot ln(2.7)}\\100=e^{t\cdot ln(2.7)}\\ln\ 100=ln\ e^{t\cdot ln(2.7)}\\ln\ 100=t\cdot ln(2.7)\\\dfrac{ln\ 100}{ln\ 2.7}=t\\\\\boxed{4.6=t}$