For translations like this use the formula:
f(x) = (x - h)² + k

where h is the lateral movement/shifts on the x-axis and k is the vertical movement/shifts on the y-axis.

Since g(x) is a movement to the right 4 units and up 9 units, your h is a positive 4 and k is a 9:

g(x) = (x - 4)² + 9

Here's a picture of your original graph f(x) and your translation g(x)

4 0

3 years ago

The population of an unknown bacteria in an experimental culture is estimated by the population function, N(x)=4800/1+99e^−0.5x,

Gnesinka [82]

The population is changing at the rate of 12 per hour at the end of 5 hours

<h3>How fast is the population changing at the end of 5 hours?</h3>

The function is given as:

N(x)=4800/1+99e^−0.5x

At the end of 5 hours, the value of x is

x = 5

So, we have:

N(5)=4800/1+99e^−0.5*5

Evaluate the product

N(5)=4800/1+99e^−0.25

Evaluate the exponent

N(5)=4800/1+99*0.779

Evaluate the product

N(5)=4800/1+77.121

Evaluate the sum

N(5)=4800/78.121

Evaluate the quotient

N(5) = 61.44

The rate is then calculated as
Rate = N(5)/5

Substitute the known values in the above equation

Rate = 61.44/5

Evaluate

Rate = 12.288

Approximate

Rate = 12

Hence, the population is changing at the rate of 12 per hour at the end of 5 hours

Read more about exponential functions at:

brainly.com/question/11464095

#SPJ1

6 0

2 years ago