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kakasveta [241]
3 years ago
11

Given an initial quantity Q0=150 and a growth rate of 7% per unit time, give a formula for the quantity Q as a function of time

t, and find the value of the quantity at t=10.
a) Assume the growth rate is not continuous. Round your answer for Q(10) to three decimal places.
Q(t)=
Q(10) =
b) Assume the growth rate is continuous. Round your answer for Q(10) to three decimal places.
Q(t)=
Q(10)=
Mathematics
1 answer:
rodikova [14]3 years ago
8 0

Answer:

Step-by-step explanation:

From the given information:

(a)

Since growth quantity is not continuous

Q(t) = 150 (1.07)^t

For t = 10

Q(10) = 150 (1.07)^{10}

\mathbf{Q(10) = 295.073}

(b)

Here, for a continuous growth rate, the growth quantity can be computed in terms of initial quantity and the growth rate.

i.e.

Q(t) = 150 e^{0.07t}

At t = 10 for a continuous growth rate;

Q(10) = 150 e^{0.07  \times 10}

Q(10) = 150 e^{0.7}

\mathbf{Q(10) = 302.063}

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