A bacteria population increases exponentially at a rate of r% each day. After 32 days, the population has increased by 309%. Find the value of r.

r=4.5% daily

Step-by-step explanation:

Exponential Growth

The natural growth of some magnitudes can be modeled by the equation:

Where P is the actual amount of the magnitude, Po is its initial amount, r is the growth rate and t is the time.

We know after t=32 days, the population has increased by 309%. Being the original population P the 100%, then the population reached 309+100= 409%.

Substitute the given values into the model function:

Simplifying:

We need to solve for r. Taking the 32nd root:

Simplifying:

Solving:

r=4.5% daily

r(0,90)(x,y) . t(-5,0)

last option

step-by-step explanation:

∆def to ∆d"e"f"

- rotate 90 counterclockwise degrees

- then translated 5 to the left (x --> x - 5)

answer is the last option