Question

The bacteria in an old piece of cheese is growing at a rate that can be modeled by y = 280 • 2^x. Determine which number represents the growth rate.

A.) 0.5
B.) 1
C.) 2
D.)280

Answer 1

Option B is correct

A number 1 represents the growth rate.

Explanation:

Using the exponential growth formula:

`y=a(1+r)^x` .....[1]

where,

a is the initial amount

r is the growth rate

x is the number of years.

As per the statement:

The bacteria in an old piece of cheese is growing at a rate that can be modeled by

y = 280 • 2^x

We can write this equation as:

`y = 280 \cdot(1+1)^x`

On comparing with equation [1] we have;

1+1 = 1+r

Subtract 1 from both sides we have;

1 = r

or

r = 1

Therefore, the growth rate is, 1.

Answer 2

The answer is C.) 2

The general form of formula is
y = a • r^x
y - the total number of bacteria after x period of time
a - the initial number of bacteria
r - growth rate
x - period of time

Let's compare:
y = a • r^x
y = 280 • 2^x

Since r = 2, the growth rate is C.) 2