Question

A group of yeast cells grows by 75% every 3hrs. At 9am, there are 200 yeast cells [9 marks].

Answer 1

a) The exponential function that models the number of cells is: $A(t) = 200(1.75)^{\frac{t}{3}}$

b) There will be 1292 cells after 10 hours.

What is an exponential function?

An increasing exponential function is modeled by:

$A(t) = A(0)(1 + r)^{\frac{t}{n}}$

In which:

• A(t) is the amount after t hours.

• A(0) is the initial amount.

• r is the rate of change, as a decimal.

• n is the time it takes to change.

For this problem, the parameters are:

A(0) = 200, r = 0.75, n = 3.

Hence the equation is:

$A(t) = A(0)(1 + r)^{\frac{t}{n}}$

$A(t) = 200(1 + 0.75)^{\frac{t}{3}}$

$A(t) = 200(1.75)^{\frac{t}{3}}$

The number of cells after 10 hours is:

$A(t) = 200(1.75)^{\frac{t}{3}}$

$A(10) = 200(1.75)^{\frac{10}{3}}$

A(10) = 1292.

More can be learned about exponential functions at brainly.com/question/25537936

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