Question

Yao is conducting a biology experiment. He uses the function f(t)=22(1.5)^t to represent the total number of bacteria over time, t, in days. Explain the meaning of 1.5 in Yao’s experiment.

Answer 1

SOLUTION

GIVEN

Yao is conducting a biology experiment.

He uses the function

$\sf{f(t) = 22 \times {(1.5)}^{t} }$

to represent the total number of bacteria over time, t, in days.

TO DETERMINE

Explain the meaning of 1.5 in Yao’s experiment.

EVALUATION

Here it is given that

$\sf{f(t) = 22 \times {(1.5)}^{t} }$

Which can be rewritten as

$\displaystyle \sf{f(t) = 22 \times {(1 + 0.5)}^{t} }$

$\displaystyle \sf{ \implies \: f(t) = 22 \times { \bigg(1 + \frac{5}{10} \bigg)}^{t} }$

$\displaystyle \sf{ \implies \: f(t) = 22 \times { \bigg(1 + \frac{50}{100} \bigg)}^{t} }$

So From above we see that

The number of bacteria at initial stage = 22

The rate of increase per days = 50%

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