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denis23 [38]
2 years ago
13

Randy walks 1/2 mile in each 1/5 hour. How far will Randy walk in one hour

Mathematics
1 answer:
katrin [286]2 years ago
7 0
In the given problem, it is already given that Randy can walk for a distance of 1/2 a mile in 1/5 of an hour. Now let us first convert 1/5 hour to minutes. this will make the problem a bit easy.
1/5 hour = 1/5 * 60 minutes
               = 12 minutes
So
Randy in 12 minutes can walk for a distance of = 1/2 mile
Then
In 60 minutes Randy can walk for a distance of = [1/(2*12)] * 60
                                                                             = (1/24) * 60
                                                                              = 2.5
So Randy can walk 2.5 miles in 1 hour.
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The question is incomplete. Here is the complete question.

Uninhibited growth can be modeled by exponential functions other than A(t)=A_{0}e^{kt}. for example, if an initial population P₀ requires n units of time to triple, then the function P(t)=P_{0}(3)^{\frac{t}{n} } models the size of the population at time t. An insect population grows exponentially. Complete the parts a through d below.

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Step-by-step explanation:

a) n is time necessary to triple the population of insects, i.e., n = 30 and P₀ = 50. So, Exponential equation for growth is

P(t)=50(3)^{\frac{t}{30} }

b) In t = 47 days:

P(t)=50(3)^{\frac{t}{30} }

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750=50(3)^{\frac{t}{30} }

\frac{750}{50}=(3)^{\frac{t}{30} }

(3)^{\frac{t}{n} }=15

Using the property <u>Power</u> <u>Rule</u> of logarithm:

log(3)^{\frac{t}{30} }=log15

\frac{t}{30}log(3)=log15

t=\frac{log15}{log3} .30

t = 74

To reach a population of 750 insects, it will take 74 days

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Use Power Rule again:

ln3=ln(e^{30k})

ln3=30k

k=\frac{ln3}{30}

k = 0.037

Equation for exponential growth will be:

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