Exercise 11 Page 298

Practice makes perfect

a We are given a function that represents the number of frogs in a pond after t years.

f(t)= 5( 4)^t The constant multiplier, 4, is greater than 1. This means it is an exponential growth function.

b To draw the graph of the function, we will make a table of values.

x	5(4)^x	y=5(4)^x
0	5(4)^0	5
1	5(4)^1	20
2	5(4)^2	80

Let's now plot and connect the points ( 0, 5), ( 1, 20), and ( 2, 80) with a smooth curve.

We can see in the graph that the range is all real numbers greater than zero. The domain of exponential functions is all real numbers. Domain:& All real numbers Range:& y>0

c We know that any exponential growth function has the form below.

y=a(1+ r)^t Here, r represents the percent change after t periods. In the given function, t represents years. f(t)=5(4)^t ⇔ f(t)=5(1+ 3)^t Therefore, the yearly percent change of the function is 3, or 300 %. To find the approximate monthly percent change, we write 112 * 12t instead of t.

f(t)=5(4)^t

Rewrite

Rewrite t as 1/12 * 12t

f(t)=5(4)^(112 * 12t)

ProdInExponent

a^(m* n)=(a^m)^n

f(t)=5(4^(112))^(12t)

▼

Simplify right-hand side

CalcPow

Calculate power

f(t)=5(1.122462 ...)^(12t)