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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)=

Respuesta :

ajeigbeibraheem

Answer:

Step-by-step explanation:

From the given information:

(a)

Since growth quantity is not continuous

[tex]Q(t) = 150 (1.07)^t[/tex]

For t = 10

[tex]Q(10) = 150 (1.07)^{10}[/tex]

[tex]\mathbf{Q(10) = 295.073}[/tex]

(b)

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

i.e.

[tex]Q(t) = 150 e^{0.07t}[/tex]

At t = 10 for a continuous growth rate;

[tex]Q(10) = 150 e^{0.07 \times 10}[/tex]

[tex]Q(10) = 150 e^{0.7}[/tex]

[tex]\mathbf{Q(10) = 302.063}[/tex]

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