Question

MULTIPLE CHOICE
An initial population of 175 quail increases at an annual rate of 22%. Write an exponential function to model the quail population. What will the approximate population be after 5 years?

A. ƒ(x) = 175(0.22)^x; 473
B. ƒ(x) = (175 • 0.22)^x; 84,587,005
C. ƒ(x) = 175(22)^x; 901,885,600
D. ƒ(x) = 175(1.22)^x; 473

Answer 1

using differential equations you should get something such as

\[P=ce^{kt}\]

at time 0, population = 175

P(0)=175

put this into the equation

\[175=ce^{k(0)}\]
\[175=c(1)=c\]

so c = 175

now we have
\[P=175e^{kt}\]

Answer 2

oh wait this is not compounded it's a flat rate umm hold on

Answer 3

so alright if you have an initial value 175, and you want to add 22 % each year. that'd mean after the first year you'd have 1.22. The only with 1.22 is your last answer

Answer 4

Exponential equations have this general form: Y=a*(b^x)
Making Y = Y(t), a = Y0, b = (1+k) and x = t, we have:

Y(t)=Y0(1+k)^t, where k is the growth rate (in decimals) dand t is the period.

Now try replacing the data and see where you get ;-)

Answer 5

1.22 isn't an answer choice though?

Answer 6

1+k=?

Answer 7

?

Answer 8

If k is the growth rate, k = 0.22, then...

Answer 9

Now try to figure what is the value of Y(0) and t

Answer 10

ok thanks