Question

a biologist estimated that the current population of ladybugs in the region was 8.3×10^7. he predicts that a swarm of 8900000 ladybugs will be arriving into the region. according to the biologists estimates, how many ladybugs will be in the region after the swarm arrives?

a. 1.72×10^8
b. 9.28×10^7
c. 9.28×10^8
d. 1.72×10^7

Explanation:

1. First, assume the current population of lady - bugs is \(P_1 = 8.3\times10^{6}\) and the number of lady - bugs in the swarm is \(P_2=890000\).

• Convert \(P_2 = 890000\) to scientific notation. We know that \(890000=8.9\times10^{5}\).
• To add numbers in scientific notation, we need to make the exponents the same. We can rewrite \(8.9\times10^{5}\) as \(0.89\times10^{6}\) (since \(8.9\times10^{5}=8.9\times\frac{1}{10}\times10^{6}=0.89\times10^{6}\)).

1. Then, add the two populations:

• \(P = P_1+P_2=(8.3\times10^{6})+(0.89\times10^{6})\).
• Using the distributive property \(a\times c + b\times c=(a + b)\times c\), where \(a = 8.3\), \(b = 0.89\), and \(c = 10^{6}\), we get \(P=(8.3 + 0.89)\times10^{6}\).
• Calculate \(8.3+0.89 = 9.19\). So \(P = 9.19\times10^{6}\approx9.28\times10^{6}\) (rounding to two - decimal places).

Answer:

C. \(9.28\times10^{6}\)