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One type of flower is growing in a pond. The flowers F in the pond are growing exponentially.

0 200
1 800

One type of flower is growing in a pond. The flowers F in the pond are growing exponentially-example-1
User Ronnefeldt
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Answer:

The function that models the number of flowers, F(t), is given as F(t) = cd, where c and d are constants. We need to find the values of c and d in order to write the equation for the number of flowers in the pond at time, t.

From the table, we know that when t=0, F(t) = 200. This means that:

F(0) = cd = 200

Similarly, when t=1, F(t) = 800. This means that:

F(1) = cd = 800

We can solve this system of equations for c and d by dividing the second equation by the first equation:

F(1)/F(0) = 800/200

4 = d/c

Now we can substitute the value of d/c into either equation to solve for one of the constants. Let's use the first equation:

cd = 200

c(d/c) = 200

d = 200/c

Substituting this into the equation d/c = 4, we get:

4 = d/c = (200/c) / c

4c = 200

c = 50

Now we can find the value of d using d = 200/c:

d = 200/50 = 4

Therefore, the equation for the number of flowers in the pond at time, t, is:

N(t) = cd = 50(4) = 200

So, the answer is N(t) = 200(1), which means that at any time t, the number of flowers in the pond is 200.

User Brandon Tom
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