Math  /  Algebra

QuestionYour answer is incorrect. The area covered by a certain population of bacteria increases according to a continuous exponential growth model. Suppose that a sample culture has an initial area of 5.6 mm25.6 \mathrm{~mm}^{2} and an observed doubling time of 5 minutes. (a) Let tt be the time (in minutes) passed, and let yy be the area of the sample at time tt. Write a formula relating yy to tt. Use exact expressions to fill in the missing parts of the formula. Do not use approximations. y=5.6e(ln25)ty=5.6 e^{\left(\frac{\ln 2}{5}\right) t} (b) What will the area of the sample be in 22 minutes?
Do not round any intermediate computations, and round your answer to the nearest tenth. 179.2 mm2179.2 \mathrm{~mm}^{2}

Studdy Solution
Calculate 24.4 2^{4.4} and then y y :
24.425.6 2^{4.4} \approx 25.6
y=5.625.6 y = 5.6 \cdot 25.6
y143.36 y \approx 143.36
Round to the nearest tenth:
y143.4mm2 y \approx 143.4 \, \text{mm}^2
The area of the sample in 22 minutes is:
143.4mm2 \boxed{143.4 \, \text{mm}^2}

View Full Solution - Free
Was this helpful?

Studdy solves anything!

banner

Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

ParentsInfluencer programContactPolicyTerms
TwitterInstagramFacebookTikTokDiscord