Question

1. a pet store employee notices that the number of fish in a specific fish tank is doubling en when he first counted the fish there were 10 fish in the tank.

c) does this situation represent linear or exponential growth? (circle one).
d) how many fish would be in the fish tank after a week? show your work below and answer in a full sentence! (3 pts)

Explanation:

Step1: Determine the type of growth

Since the number of fish is doubling each week (multiplicative change), it is exponential growth.

Step2: Set up the exponential growth formula

The formula for exponential growth is \(y = a\times b^{x}\), where \(a = 10\) (initial number of fish), \(b = 2\) (growth factor as it doubles), and \(x\) is the number of weeks. After \(x = 7\) weeks (a week has 7 days, assuming the doubling is weekly), we substitute into the formula: \(y=10\times2^{7}\).

Step3: Calculate \(2^{7}\)

\(2^{7}=2\times2\times2\times2\times2\times2\times2 = 128\).

Step4: Find the value of \(y\)

\(y = 10\times128=1280\).

Answer:

c) Exponential growth.
d) The number of fish in the tank after a week is \(1280\).