An experimental population of fruit flies increases according to the law of exponential growth. There were 60 flies after the 2nd day of the experiment and 360 flies after the fourth day. How many flies were there in the original population?

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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step-by-step explanation:

, and

for

step-by-step explanation:

we can analyze the pattern at which the terms increase. let us denote , , , so that we can call

note the following:

the pattern: to get the next term value, we just add the next term number (e.g. 1st, 2nd, to the previous term value (term values are the given numbers in the question, 1, 3, 6, 10, 15,

from , to get to , we add

from , to get to , we add

etc.

we need to form a recursive formula, a formula that has the next term as a function of the previous term. so a possible recursive formula can be

, and for