the height of a plant was 204 millimeters. after one week, it grew by 33 millimeters, and after 3 more weeks, the new height of the plant was 282 millimeters. how much did the plant grow in 3 weeks?

Answer 1

P=204

each week grows by 33

when 3+1= 4 weeks it's 284

A=P(1+r)^t

237 = 204(1+r)

284=204(1+r)^4

in 4 weeks it grew 284-204 = 80 mm

usually plants grow continuously meaning use the compounding continuously formula

A=Pe^rt

284=204e^4r

284/204= 71/51e^4r

ln(71/51)= 4r

r = (ln(71/51)4

in 4 weeks

A=204e^ln(71/51)

A=204(71/51)= 284 mm

in 3 weeks

A=204e^(3/4)ln(71/51)

= about 261.4546 mm

in 3 weeks it grew 261- 204 = about 57 mm