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hoa [83]
3 years ago
10

An experimental population of fruit flies increases according to the law of exponential growth. There were 60 flies after the 2n

d day of the experiment and 360 flies after the fourth day. How many flies were there in the original population?
Mathematics
1 answer:
Mice21 [21]3 years ago
3 0

Answer:

There were 10 flies originally

Step-by-step explanation:

Since we have an exponential growth, we will be having a constant percentage of increase and we can set up the increase at any day using the following equation;

V = I(1+r)^d

where V is the number of flies on a particular day

I is the initial number of flies

r is the constant increase in percentage

and d is the number of days.

So we have for the second day;

60 = I(1+r)^2 ••••••(i)

For the fourth day, we have;

360 = I(1+r)^4 ••••••••(ii)

divide equation ii by i; we have;

360/60 = (1+r)^4/(1+r)^2

6 = (1+r)^2

(√6)^2 = (1+r)^2

1 + r = √6

r = √6 - 1

So we can substitute the value of r in any of the equations to get I which is the initial number of flies

Let’s use equation 1

60 = I(1 + r)^2

60 = I(1 + √6 -1)^2

60 = I(√6)^2

60 = 6I

I = 60/6

I = 10 flies

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