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Answer 1

Answer:  Approximately 191 bees

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Work Shown:

One way to express exponential form is to use

y = a*b^x

where 'a' is the initial value and 'b' is linked to the growth rate.

Since we're told 34 bees are there initially, we know a = 34.

Then after 4 days, we have 48 bees. So we can say,

y = a*b^x

y = 34*b^x

48 = 34*b^4

48/34 = b^4

24/17 = b^4

b^4 = 24/17

b = (24/17)^(1/4)

b = 1.090035

Which is approximate.

The function updates to

y = a*b^x

y = 34*(1.090035)^x

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As a way to check to see if we have the right function, plug in x = 0 and we find:

y = 34*(1.090035)^x

y = 34*(1.090035)^0

y = 34*(1)

y = 34

So there are 34 bees on day 0, ie the starting day.

Plug in x = 4

y = 34*(1.090035)^x

y = 34*(1.090035)^4

y = 34*1.4117629

y = 47.9999386

Due to rounding error we don't land on 48 exactly, but we can round to this value.

We see that after 4 days, there are 48 bees.

So we confirmed the correct exponential function.

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At this point we can find out how many bees there are expected to be after 20 days.

Plug in x = 20 to get

y = 34*(1.090035)^x

y = 34*(1.090035)^20

y = 190.672374978452

Round to the nearest whole number to get 191.

There are expected to be roughly 191 bees on day 20.