Which does not represent exponential decay?

To find the equation that best models the exponential growth function in this situation, let's analyze the given information step by step:

Step 1: Evaluate the options one by one.

Option 1: OP(t) = 7,200(0.97)
This option suggests that the population decreases by 3% each year. However, from the provided data, we can see that the population is increasing, not decreasing. Therefore, this equation does not accurately model the situation.

Option 2: O P(1) - 0.3(7,200)
In this option, the population on January 1st is subtracted by 0.3 times the initial population. However, this equation does not represent an exponential growth function. It appears to be a linear equation with a constant decrease of 0.3 times the initial population, which does not match the given data. Therefore, this option is incorrect.

Option 3: O P(1) - 7,200(1.03)
Similar to the second option, this equation subtracts the initial population by 7,200 times 1.03. Again, this does not represent exponential growth but rather a linear equation with a constant increase. Hence, this option is incorrect.

Option 4: OP(t) = 7,200(1.03)
This option suggests that the population increases by 3% each year. Let's check if this equation accurately models the situation.

Step 2: Calculate the growth factor.

To calculate the growth factor, we divide the population of each subsequent year by the population of the previous year.

For 2005 to 2006: Growth factor = 7,416 / 7,200 = 1.03 (approximately)
For 2006 to 2007: Growth factor = 7,639 / 7,416 ≈ 1.03 (approximately)
For 2007 to 2008: Growth factor = 7,867 / 7,639 ≈ 1.03 (approximately)

Since the growth factor is approximately 1.03 for each year, this option accurately models the situation as an exponential growth function.

Step 3: Determine the correct equation.

Based on the analysis, the correct equation that models the exponential growth function in this situation is:

OP(t) = 7,200(1.03)

This equation represents the population (OP) as a function of time (t), with an initial population of 7,200 and a growth rate of 3% per year.

Please let me know if you need further assistance or if you have any additional questions!

Exponential decay is whenever the rate^2<1.  So exponential growth occurs whenever r^2>1.

In this case only y=5(4^x) is exponential growth as 4 is greater than 1

When a decimal is multiplied to a power, it decreases exponentially. Therefore, y=3(0.2)^x does NOT represent exponential growth.

When a decimal is multiplied to a power, it decreases exponentially. Therefore, y=3(0.2)^x does NOT represent exponential growth.

B
Because the its follows the pattern also b isn’t negative

B
Because the its follows the pattern also b isn’t negative

Sure, let's go through this problem step by step:

1. In the first five days, Organism A's population doubles each day. Therefore, with each passing day, the rate of growth is multiplied by 2. Since this process happens for 5 days, we can represent the growth as an exponential expression 2^5. This indicates that organism A's population size has grown 32 times its initial size.

2. Over the next 3 days, the population of Organism A decreases by half each day due to a virus. This can be written as (2^(-1))^3, which indicates dividing the population by 2 each day. Simplifying the exponent gives 2^(-3), meaning the population would be 1/8 of what it was at the end of day 5.

3. To get the total change in organism A's population over the 8 days, we combine the increase (2^5) and decrease (2^-3). We do that by multiplying these two together: 2^5 * 2^(-3). Using the rule of multiplying with the same base, we add the exponents: 2^(5-3) = 2^2. So, the population of organism A increases by a factor of 4 times its initial size over the 8-day period.

4. Organism B's population doubles every day for 8 days and isn't affected by the virus. The exponential expression representing this growth is 2^8. This means organism B's population size has grown 256 times its initial size.

5. To find the size difference between organism B's and A's population after 8 days, we divide the population size of organism B by that of organism A. That gives us 2^8 / 2^2. Using the rule of division with the same base, we subtract the exponents: 2^(8-2) = 2^6. As a number not in exponential form, that's 64.

So, Organism B's population is 64 times larger than organism A's after 8 days.

Remember to carefully follow all the advised steps such as double-checking work at each step, careful cancellation of terms in fractions, paying close attention to signs, verifying the final answer and accuracy in factoring expressions.

The formula of the function would be:
y = 96000(1.07)^t

The graph is an exponential function with y-intercept of 9600. The curve goes upward indefinitely as the value of time increases.

Therefore, from the choices, the statements that apply to the graph are:
-The graph of the function begins at y = 96,000.
-The graph of the function shows the exponential growth.