Question

Kirk made the graph to show his prediction of a population of bacteria over time. Which function best models the data in the graph?
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Jana predicts that the population, y, will grow according to y = 12 log(x + 1) + 10, where x is the time in minutes. How much greater does Kirk’s model predict the population will be after 60 minutes than Jana’s model?
✔ greater by about 50 bacteria

Answer 1

Answer:

greater by about 50 bacteria

hope this helps,

T

Step-by-step explanation:

Answer 2

Populations can be modeled by exponential functions and logarithm functions.

• Kirk's function is: $\mathbf{f(x) = (10)2^{\frac{x}{20}}}$
• Kirk’s model predict the population will be greater than about 50 bacteria after 60 minutes than Jana’s model

Kirk's graph is an exponential function, and it is represented as:

$\mathbf{y = ab^x}$

From the graph (see attachment);

x = 0, when y =10.

So, we have:

$\mathbf{10 = ab^0}$

$\mathbf{10 = a\times 1}$

$\mathbf{10 = a}$

Rewrite as:

$\mathbf{a = 10 }$

Substitute $\mathbf{a = 10 }$ in $\mathbf{y = ab^x}$

So, we have:

$\mathbf{y = 10(b)^x}$

x = 20, when y =20.

$\mathbf{20 = 10(b)^{20}}$

Divide both sides by 10

$\mathbf{2 = b^{20}}$

Take 20th root of both sides

$\mathbf{b = 2^{\frac{1}{20}}}$

Substitute $\mathbf{b = 2^{\frac{1}{20}}}$ in $\mathbf{y = 10(b)^x}$

$\mathbf{y = 10(2^{\frac{1}{20}})^x}$

$\mathbf{y = (10)2^{\frac{x}{20}}}$

Represent as function

$\mathbf{f(x) = (10)2^{\frac{x}{20}}}$

So, Kirk's function is: $\mathbf{f(x) = (10)2^{\frac{x}{20}}}$

When x = 60, we have:

$\mathbf{f(60) = (10)2^{\frac{60}{20}}}$

$\mathbf{f(60) = (10)2^3}$

$\mathbf{f(60) = (10)8}$

$\mathbf{f(60) = 80}$ ---- Kirk's model

For Jana's model, we have:

$\mathbf{y = 12log(x + 1) + 10}$

Substitute 60 for x

$\mathbf{y = 12log(60 + 1) + 10}$

$\mathbf{y = 12log(61) + 10}$

Using a calculator, we have:

$\mathbf{y \approx 31}$ --- Jana's model

Calculate the difference between both models

$\mathbf{d = 80 - 31}$

$\mathbf{d = 49}$

Approximate

$\mathbf{d \approx 50}$

Hence, Kirk’s model predict the population will be greater than about 50 bacteria after 60 minutes than Jana’s model

Read more about population models at:

https://brainly.com/question/8993571