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3 years ago

6

A mother is 3 times as old as her daughter.In 12 years time she will be twice as old as her daughter will be then. How old is th

e mother now?

2 answers:

andrezito [222]3 years ago

8 0

Answer:

<em>The mother will be 36.</em>

Step-by-step explanation:

Novay_Z [31]3 years ago

6 0

Answer:

36

Step-by-step explanation:

just multiply 12 and 3

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mars1129 [50]

Answer:

(a) $P_{t}=3(2)^{6t}$

(b) $3(2)^{42}$

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Step-by-step explanation:

A cell of some bacteria divides itself into 2 cells in every 10 minutes and initial population of the bacteria was 3.

That means sequence formed will be 3, 6, 12, 24............

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Now we know the explicit formula of a geometric sequence is given by

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Where a = Initial population = 3 bacteria

r = common ratio = 2

and t = time in hours

So explicit formula will be $P_{t}=3(2)^{6t}$

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$P_{t}=3(2)^{6t}$

(b) We have to find the size of population after 7 hours or 420 minutes

$P_{t}=3(2)^{6\times7}$

= $3(2)^{42}$

After 7 hours bacteria population will be $3(2)^{42}$

(c) Time to reach population as 21

By the explicit formula

$21=3(2)^{6t}$

$2^{6t}=\frac{21}{3}=7$

Now we take log on both the sides of the equation

$log(2^{6t})=log(7)$

6t log2 = log 7

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t(1.806) = 0.845

t = $\frac{0.845}{1.806}=0.468$ hours

Or t = 0.468×60 = 28.07 minutes

Therefore, after 28.07 minutes bacterial population will be 21

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3 years ago